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LSAT Formal Logic Exercise

JohnMaynardKeynes
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7/1/2014 5:16:14 PM
Posted: 2 years ago
I came across this exercise on the internet, and disagree quite a bit with the answer. I was hoping to get some thoughts on it. It can be found here: http://grockit.com...

Jacques will run for class president unless Mitzi runs for class president. Which of the following is/are IMPOSSIBLE? [Choose all that apply]

(i)-Jacques runs for class president unopposed.
(ii)-Mitzi runs for class president unopposed.
(iii)-Only Jacques and Mitzi run for class president.
(iv)-Eleanor runs for class president unopposed.
(v)-No one runs for class president.


My reasoning was that i and ii are both possible; Jacques and Mitzi running are two mutually exclusive events, so it's possible that either of them could run unopposed.

I also found iv and v fairly straight-forward: both are impossible. Iv is impossible because either Jacques or Mitzi are going to run, meaning that another person wouldn't be able to run unopposed. The same logic extends to V.

So far, everything I have reasoned is correct, according to the answer key. The controversy comes in with answer iii. It suggests that both Jacques and Mitzi will run. But how is this possible? Jacques and Mitzi running are two mutually exclusive events, are they not? "Jacques will run unless Mitzi runs" or X unless Y. In order words, if Y occurs, X cannot. How, then, is iii possible?

Any thoughts?
~JohnMaynardKeynes

"The sight of my succulent backside acts as a sedative for the beholder. It soothes the pain of life and makes all which hurts seem like bliss. I urge all those stressed by ridiculous drama on DDO which will never affect your real life to gaze upon my cheeks for they will make you have an excitement and joy you've never felt before." -- Dr. Dennybug

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Stand with Dogs and Economics
bossyburrito
Posts: 14,075
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7/1/2014 5:24:13 PM
Posted: 2 years ago
The explanation they gave was utterly ridiculous - If you consider A and B, if the statement "A is blue UNLESS B is green", it's completely obvious that, in the case that B is green, A CANNOT be blue.

The only way they could argue otherwise is if they use some weird semantic trick and say that "unless" would just result in A not necessarily being blue, but that the possibility would still remain (which I think is abusive to the English language, really).
#UnbanTheMadman

"Some will sell their dreams for small desires
Or lose the race to rats
Get caught in ticking traps
And start to dream of somewhere
To relax their restless flight
Somewhere out of a memory of lighted streets on quiet nights..."

~ Rush
JohnMaynardKeynes
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7/1/2014 5:25:21 PM
Posted: 2 years ago
At 7/1/2014 5:24:13 PM, bossyburrito wrote:
The explanation they gave was utterly ridiculous - If you consider A and B, if the statement "A is blue UNLESS B is green", it's completely obvious that, in the case that B is green, A CANNOT be blue.

The only way they could argue otherwise is if they use some weird semantic trick and say that "unless" would just result in A not necessarily being blue, but that the possibility would still remain (which I think is abusive to the English language, really).

I was thinking the same thing. "Unless" could indicate a possible exception, as you said, but not designate that the two events are mutually exclusive.
~JohnMaynardKeynes

"The sight of my succulent backside acts as a sedative for the beholder. It soothes the pain of life and makes all which hurts seem like bliss. I urge all those stressed by ridiculous drama on DDO which will never affect your real life to gaze upon my cheeks for they will make you have an excitement and joy you've never felt before." -- Dr. Dennybug

Founder of the BSH-YYW Fan Club
Founder of the Barkalotti
Stand with Dogs and Economics
sadolite
Posts: 8,839
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7/3/2014 7:20:22 PM
Posted: 2 years ago
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:
I came across this exercise on the internet, and disagree quite a bit with the answer. I was hoping to get some thoughts on it. It can be found here: http://grockit.com...

Jacques will run for class president unless Mitzi runs for class president. Which of the following is/are IMPOSSIBLE? [Choose all that apply]

(i)-Jacques runs for class president unopposed.
(ii)-Mitzi runs for class president unopposed.
(iii)-Only Jacques and Mitzi run for class president.
(iv)-Eleanor runs for class president unopposed.
(v)-No one runs for class president.


My reasoning was that i and ii are both possible; Jacques and Mitzi running are two mutually exclusive events, so it's possible that either of them could run unopposed.

I also found iv and v fairly straight-forward: both are impossible. Iv is impossible because either Jacques or Mitzi are going to run, meaning that another person wouldn't be able to run unopposed. The same logic extends to V.

So far, everything I have reasoned is correct, according to the answer key. The controversy comes in with answer iii. It suggests that both Jacques and Mitzi will run. But how is this possible? Jacques and Mitzi running are two mutually exclusive events, are they not? "Jacques will run unless Mitzi runs" or X unless Y. In order words, if Y occurs, X cannot. How, then, is iii possible?

Any thoughts?

This isn't logic, it's a waste of life and minutes of your life you can never get back just thinking about it. The logical answer is who's names are on the ballot. and who ever gets the most votes wins . Nothing else matters.
It's not your views that divide us, it's what you think my views should be that divides us.

If you think I will give up my rights and forsake social etiquette to make you "FEEL" better you are sadly mistaken

If liberal democrats would just stop shooting people gun violence would drop by 90%
Khaos_Mage
Posts: 23,214
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7/6/2014 6:31:01 AM
Posted: 2 years ago
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:

Jacques will run for class president unless Mitzi runs for class president. Which of the following is/are IMPOSSIBLE? [Choose all that apply]

(i)-Jacques runs for class president unopposed.
(ii)-Mitzi runs for class president unopposed.
(iii)-Only Jacques and Mitzi run for class president.
Any thoughts?


The issue is the word "and".
In this context, poorly worded IMO, the answer is stating that the field will consist only of those two potential outcomes (i.e. only one of Jacques and Mitzi will run, and no one else)
My work here is, finally, done.
Khaos_Mage
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7/6/2014 6:41:32 AM
Posted: 2 years ago
At 7/1/2014 5:25:21 PM, JohnMaynardKeynes wrote:
At 7/1/2014 5:24:13 PM, bossyburrito wrote:
The explanation they gave was utterly ridiculous - If you consider A and B, if the statement "A is blue UNLESS B is green", it's completely obvious that, in the case that B is green, A CANNOT be blue.

The only way they could argue otherwise is if they use some weird semantic trick and say that "unless" would just result in A not necessarily being blue, but that the possibility would still remain (which I think is abusive to the English language, really).

I was thinking the same thing. "Unless" could indicate a possible exception, as you said, but not designate that the two events are mutually exclusive.

After reading the answer, it is equally nuanced.
X unless Y, implies non-certainty, due to the possibility of an outcome (Mitzi running). A practical example would be Jacques would have to know that Mitzi is running. If he didn't know, then they'd both be running (and technically, they'd both be running for some amount of time, between Mitzi's hat being thrown and Jacques conceding).

Plus, I still like my and response.
I don't quite understand the cab example...
My work here is, finally, done.
Wocambs
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7/6/2014 5:42:36 PM
Posted: 2 years ago
At 7/1/2014 5:25:21 PM, JohnMaynardKeynes wrote:
At 7/1/2014 5:24:13 PM, bossyburrito wrote:
The explanation they gave was utterly ridiculous - If you consider A and B, if the statement "A is blue UNLESS B is green", it's completely obvious that, in the case that B is green, A CANNOT be blue.

The only way they could argue otherwise is if they use some weird semantic trick and say that "unless" would just result in A not necessarily being blue, but that the possibility would still remain (which I think is abusive to the English language, really).

I was thinking the same thing. "Unless" could indicate a possible exception, as you said, but not designate that the two events are mutually exclusive.

Unless indicates an exception, so I think it necessitates that they exclude each other here. Jacques will run for president is the rule, but if Mitzi runs then an exception will be made to that rule, so Jacques will not run. Right?

'"I will call a cab unless my mom remembers to pick us up." Notice that even if mom does remember, we may decide we"d just as soon call a cab.' is complete nonsense since if his mother does remember and he calls a cab anyway then he's contradicted himself. Might as well say 'I won't drink the milk unless it's lactose free' and then drink it upon discovering that it contains lactose.
bossyburrito
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7/6/2014 5:46:05 PM
Posted: 2 years ago
Sadolite hit the nail on the head - it's a waste of time.
#UnbanTheMadman

"Some will sell their dreams for small desires
Or lose the race to rats
Get caught in ticking traps
And start to dream of somewhere
To relax their restless flight
Somewhere out of a memory of lighted streets on quiet nights..."

~ Rush
JohnMaynardKeynes
Posts: 1,512
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7/6/2014 5:46:19 PM
Posted: 2 years ago
At 7/6/2014 5:42:36 PM, Wocambs wrote:
At 7/1/2014 5:25:21 PM, JohnMaynardKeynes wrote:
At 7/1/2014 5:24:13 PM, bossyburrito wrote:
The explanation they gave was utterly ridiculous - If you consider A and B, if the statement "A is blue UNLESS B is green", it's completely obvious that, in the case that B is green, A CANNOT be blue.

The only way they could argue otherwise is if they use some weird semantic trick and say that "unless" would just result in A not necessarily being blue, but that the possibility would still remain (which I think is abusive to the English language, really).

I was thinking the same thing. "Unless" could indicate a possible exception, as you said, but not designate that the two events are mutually exclusive.

Unless indicates an exception, so I think it necessitates that they exclude each other here. Jacques will run for president is the rule, but if Mitzi runs then an exception will be made to that rule, so Jacques will not run. Right?

'"I will call a cab unless my mom remembers to pick us up." Notice that even if mom does remember, we may decide we"d just as soon call a cab.' is complete nonsense since if his mother does remember and he calls a cab anyway then he's contradicted himself. Might as well say 'I won't drink the milk unless it's lactose free' and then drink it upon discovering that it contains lactose.

I had a similar case initially, and on a fundamental level I completely agree with you. The way the prompt asks us to think of "except" is completely unconventional. But I think what they were hoping we would do -- and, frankly, this is inductive from learning of the answer -- is reason that "X unless Y" suggests that X will occur provided that Y doesn't, i.e., Y may prevent X, but we don't have reason to believe that X and Y are mutually exclusive. I'm trying to think of a formulation where we could conclude that they are, but thus far I've had no luck.

I'm honestly tempted to take a vote on this question. I feel that most people would probably agree with you that the events should be mutually exclusive.
~JohnMaynardKeynes

"The sight of my succulent backside acts as a sedative for the beholder. It soothes the pain of life and makes all which hurts seem like bliss. I urge all those stressed by ridiculous drama on DDO which will never affect your real life to gaze upon my cheeks for they will make you have an excitement and joy you've never felt before." -- Dr. Dennybug

Founder of the BSH-YYW Fan Club
Founder of the Barkalotti
Stand with Dogs and Economics
Wocambs
Posts: 1,505
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7/6/2014 6:07:27 PM
Posted: 2 years ago
At 7/6/2014 5:46:19 PM, JohnMaynardKeynes wrote:
At 7/6/2014 5:42:36 PM, Wocambs wrote:
At 7/1/2014 5:25:21 PM, JohnMaynardKeynes wrote:
At 7/1/2014 5:24:13 PM, bossyburrito wrote:
The explanation they gave was utterly ridiculous - If you consider A and B, if the statement "A is blue UNLESS B is green", it's completely obvious that, in the case that B is green, A CANNOT be blue.

The only way they could argue otherwise is if they use some weird semantic trick and say that "unless" would just result in A not necessarily being blue, but that the possibility would still remain (which I think is abusive to the English language, really).

I was thinking the same thing. "Unless" could indicate a possible exception, as you said, but not designate that the two events are mutually exclusive.

Unless indicates an exception, so I think it necessitates that they exclude each other here. Jacques will run for president is the rule, but if Mitzi runs then an exception will be made to that rule, so Jacques will not run. Right?

'"I will call a cab unless my mom remembers to pick us up." Notice that even if mom does remember, we may decide we"d just as soon call a cab.' is complete nonsense since if his mother does remember and he calls a cab anyway then he's contradicted himself. Might as well say 'I won't drink the milk unless it's lactose free' and then drink it upon discovering that it contains lactose.

I had a similar case initially, and on a fundamental level I completely agree with you. The way the prompt asks us to think of "except" is completely unconventional. But I think what they were hoping we would do -- and, frankly, this is inductive from learning of the answer -- is reason that "X unless Y" suggests that X will occur provided that Y doesn't, i.e., Y may prevent X, but we don't have reason to believe that X and Y are mutually exclusive. I'm trying to think of a formulation where we could conclude that they are, but thus far I've had no luck.

I'm honestly tempted to take a vote on this question. I feel that most people would probably agree with you that the events should be mutually exclusive.

From 'mom"s remembering is a possible exception to the taxi call, but ONLY a possible one' I think I know what they're trying to say, but they're still wrong.

Mitzi's running is a possible exception to Jacques running, but this is only because other things could prevent Jacques running, such as someone blowing his head off. Thus, it is true that Mitzi's running can only be said to possibly prevent Jacques from running, not 'definitely prevent' Jacques from running, but this is due to causation (what is responsible) and has absolutely nothing to do with the end result, because Mitzi could run but not prevent Jacques, because Eleanor already prevented him from running by shooting him. For some reason they have misinterpreted this to reach the conclusion that Jacques may still run even if Mitzi does.

They have decided that because Mitzi doesn't necessarily prevent Jacques from running that they could run together, despite Mitzi's running making it impossible for Jacques to run, because they have gotten confused about what it means for Mitzi's running to be a 'possible exception'. I think the actual mistake that they're attempt at clever wording would produce is 'Jacques will run unless Mitzi runs - Mitzi does not run, will Jacques run?', the mistake being to answer 'yes'. It's a stupid question just like saying 'The dog will bark if there is an intruder. There is an intruder. Does the dog bark? No, because he's asleep'.
wrichcirw
Posts: 11,196
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7/7/2014 4:55:55 AM
Posted: 2 years ago
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:
I came across this exercise on the internet, and disagree quite a bit with the answer. I was hoping to get some thoughts on it. It can be found here: http://grockit.com...

Jacques will run for class president unless Mitzi runs for class president. Which of the following is/are IMPOSSIBLE? [Choose all that apply]

(i)-Jacques runs for class president unopposed.
(ii)-Mitzi runs for class president unopposed.
(iii)-Only Jacques and Mitzi run for class president.
(iv)-Eleanor runs for class president unopposed.
(v)-No one runs for class president.


My reasoning was that i and ii are both possible; Jacques and Mitzi running are two mutually exclusive events, so it's possible that either of them could run unopposed.

I also found iv and v fairly straight-forward: both are impossible. Iv is impossible because either Jacques or Mitzi are going to run, meaning that another person wouldn't be able to run unopposed. The same logic extends to V.

So far, everything I have reasoned is correct, according to the answer key. The controversy comes in with answer iii. It suggests that both Jacques and Mitzi will run. But how is this possible? Jacques and Mitzi running are two mutually exclusive events, are they not? "Jacques will run unless Mitzi runs" or X unless Y. In order words, if Y occurs, X cannot. How, then, is iii possible?

Any thoughts?

The underlined is the flaw in an otherwise well-reasoned explanation. X unless Y is the same as "if Y does NOT occur, X occurs", i.e. nY=>X

http://www.alphascore.com...

Contrapositive is nX=>Y.

Neither of these statements imply mutual exclusivity...there is no necessary condition as to what happens "if X" or "if Y", and so there is no statement of exclusion for either condition.

For me, the most convincing part of the link was the explanation that began "You can also look at Unless as essentially the same as saying "IF NOT""

Good luck on the LSAT.
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
dylancatlow
Posts: 12,251
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7/7/2014 4:34:01 PM
Posted: 2 years ago
At 7/7/2014 4:55:55 AM, wrichcirw wrote:
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:
I came across this exercise on the internet, and disagree quite a bit with the answer. I was hoping to get some thoughts on it. It can be found here: http://grockit.com...

Jacques will run for class president unless Mitzi runs for class president. Which of the following is/are IMPOSSIBLE? [Choose all that apply]

(i)-Jacques runs for class president unopposed.
(ii)-Mitzi runs for class president unopposed.
(iii)-Only Jacques and Mitzi run for class president.
(iv)-Eleanor runs for class president unopposed.
(v)-No one runs for class president.


My reasoning was that i and ii are both possible; Jacques and Mitzi running are two mutually exclusive events, so it's possible that either of them could run unopposed.

I also found iv and v fairly straight-forward: both are impossible. Iv is impossible because either Jacques or Mitzi are going to run, meaning that another person wouldn't be able to run unopposed. The same logic extends to V.

So far, everything I have reasoned is correct, according to the answer key. The controversy comes in with answer iii. It suggests that both Jacques and Mitzi will run. But how is this possible? Jacques and Mitzi running are two mutually exclusive events, are they not? "Jacques will run unless Mitzi runs" or X unless Y. In order words, if Y occurs, X cannot. How, then, is iii possible?

Any thoughts?

The underlined is the flaw in an otherwise well-reasoned explanation. X unless Y is the same as "if Y does NOT occur, X occurs", i.e. nY=>X

http://www.alphascore.com...

Contrapositive is nX=>Y.

Neither of these statements imply mutual exclusivity...there is no necessary condition as to what happens "if X" or "if Y", and so there is no statement of exclusion for either condition.

How does those statement not imply mutual exclusivity? If X, not Y. If Y, not X. They are clearly mutually exclusive.


For me, the most convincing part of the link was the explanation that began "You can also look at Unless as essentially the same as saying "IF NOT""

Good luck on the LSAT.
wrichcirw
Posts: 11,196
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7/7/2014 4:35:40 PM
Posted: 2 years ago
At 7/7/2014 4:34:01 PM, dylancatlow wrote:
At 7/7/2014 4:55:55 AM, wrichcirw wrote:
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:
I came across this exercise on the internet, and disagree quite a bit with the answer. I was hoping to get some thoughts on it. It can be found here: http://grockit.com...

Jacques will run for class president unless Mitzi runs for class president. Which of the following is/are IMPOSSIBLE? [Choose all that apply]

(i)-Jacques runs for class president unopposed.
(ii)-Mitzi runs for class president unopposed.
(iii)-Only Jacques and Mitzi run for class president.
(iv)-Eleanor runs for class president unopposed.
(v)-No one runs for class president.


My reasoning was that i and ii are both possible; Jacques and Mitzi running are two mutually exclusive events, so it's possible that either of them could run unopposed.

I also found iv and v fairly straight-forward: both are impossible. Iv is impossible because either Jacques or Mitzi are going to run, meaning that another person wouldn't be able to run unopposed. The same logic extends to V.

So far, everything I have reasoned is correct, according to the answer key. The controversy comes in with answer iii. It suggests that both Jacques and Mitzi will run. But how is this possible? Jacques and Mitzi running are two mutually exclusive events, are they not? "Jacques will run unless Mitzi runs" or X unless Y. In order words, if Y occurs, X cannot. How, then, is iii possible?

Any thoughts?

The underlined is the flaw in an otherwise well-reasoned explanation. X unless Y is the same as "if Y does NOT occur, X occurs", i.e. nY=>X

http://www.alphascore.com...

Contrapositive is nX=>Y.

Neither of these statements imply mutual exclusivity...there is no necessary condition as to what happens "if X" or "if Y", and so there is no statement of exclusion for either condition.

How does those statement not imply mutual exclusivity? If X, not Y. If Y, not X. They are clearly mutually exclusive.

Because those are not the statements relevant to the question. Please reread my explanation, especially the underlined. Pay attention to detail.

For me, the most convincing part of the link was the explanation that began "You can also look at Unless as essentially the same as saying "IF NOT""

Good luck on the LSAT.
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
dylancatlow
Posts: 12,251
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7/7/2014 4:36:43 PM
Posted: 2 years ago
At 7/7/2014 4:35:40 PM, wrichcirw wrote:
At 7/7/2014 4:34:01 PM, dylancatlow wrote:
At 7/7/2014 4:55:55 AM, wrichcirw wrote:
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:
I came across this exercise on the internet, and disagree quite a bit with the answer. I was hoping to get some thoughts on it. It can be found here: http://grockit.com...

Jacques will run for class president unless Mitzi runs for class president. Which of the following is/are IMPOSSIBLE? [Choose all that apply]

(i)-Jacques runs for class president unopposed.
(ii)-Mitzi runs for class president unopposed.
(iii)-Only Jacques and Mitzi run for class president.
(iv)-Eleanor runs for class president unopposed.
(v)-No one runs for class president.


My reasoning was that i and ii are both possible; Jacques and Mitzi running are two mutually exclusive events, so it's possible that either of them could run unopposed.

I also found iv and v fairly straight-forward: both are impossible. Iv is impossible because either Jacques or Mitzi are going to run, meaning that another person wouldn't be able to run unopposed. The same logic extends to V.

So far, everything I have reasoned is correct, according to the answer key. The controversy comes in with answer iii. It suggests that both Jacques and Mitzi will run. But how is this possible? Jacques and Mitzi running are two mutually exclusive events, are they not? "Jacques will run unless Mitzi runs" or X unless Y. In order words, if Y occurs, X cannot. How, then, is iii possible?

Any thoughts?

The underlined is the flaw in an otherwise well-reasoned explanation. X unless Y is the same as "if Y does NOT occur, X occurs", i.e. nY=>X

http://www.alphascore.com...

Contrapositive is nX=>Y.

Neither of these statements imply mutual exclusivity...there is no necessary condition as to what happens "if X" or "if Y", and so there is no statement of exclusion for either condition.

How does those statement not imply mutual exclusivity? If X, not Y. If Y, not X. They are clearly mutually exclusive.

Because those are not the statements relevant to the question. Please reread my explanation, especially the underlined. Pay attention to detail.

For me, the most convincing part of the link was the explanation that began "You can also look at Unless as essentially the same as saying "IF NOT""

Good luck on the LSAT.

Your explanation makes no sense whatsoever.
wrichcirw
Posts: 11,196
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7/7/2014 4:37:23 PM
Posted: 2 years ago
At 7/7/2014 4:36:43 PM, dylancatlow wrote:
At 7/7/2014 4:35:40 PM, wrichcirw wrote:
At 7/7/2014 4:34:01 PM, dylancatlow wrote:
At 7/7/2014 4:55:55 AM, wrichcirw wrote:
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:
I came across this exercise on the internet, and disagree quite a bit with the answer. I was hoping to get some thoughts on it. It can be found here: http://grockit.com...

Jacques will run for class president unless Mitzi runs for class president. Which of the following is/are IMPOSSIBLE? [Choose all that apply]

(i)-Jacques runs for class president unopposed.
(ii)-Mitzi runs for class president unopposed.
(iii)-Only Jacques and Mitzi run for class president.
(iv)-Eleanor runs for class president unopposed.
(v)-No one runs for class president.


My reasoning was that i and ii are both possible; Jacques and Mitzi running are two mutually exclusive events, so it's possible that either of them could run unopposed.

I also found iv and v fairly straight-forward: both are impossible. Iv is impossible because either Jacques or Mitzi are going to run, meaning that another person wouldn't be able to run unopposed. The same logic extends to V.

So far, everything I have reasoned is correct, according to the answer key. The controversy comes in with answer iii. It suggests that both Jacques and Mitzi will run. But how is this possible? Jacques and Mitzi running are two mutually exclusive events, are they not? "Jacques will run unless Mitzi runs" or X unless Y. In order words, if Y occurs, X cannot. How, then, is iii possible?

Any thoughts?

The underlined is the flaw in an otherwise well-reasoned explanation. X unless Y is the same as "if Y does NOT occur, X occurs", i.e. nY=>X

http://www.alphascore.com...

Contrapositive is nX=>Y.

Neither of these statements imply mutual exclusivity...there is no necessary condition as to what happens "if X" or "if Y", and so there is no statement of exclusion for either condition.

How does those statement not imply mutual exclusivity? If X, not Y. If Y, not X. They are clearly mutually exclusive.

Because those are not the statements relevant to the question. Please reread my explanation, especially the underlined. Pay attention to detail.

For me, the most convincing part of the link was the explanation that began "You can also look at Unless as essentially the same as saying "IF NOT""

Good luck on the LSAT.

Your explanation makes no sense whatsoever.

Then you should not be taking the LSAT.
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
dylancatlow
Posts: 12,251
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7/7/2014 4:45:59 PM
Posted: 2 years ago
At 7/7/2014 4:37:23 PM, wrichcirw wrote:
At 7/7/2014 4:36:43 PM, dylancatlow wrote:
At 7/7/2014 4:35:40 PM, wrichcirw wrote:
At 7/7/2014 4:34:01 PM, dylancatlow wrote:
At 7/7/2014 4:55:55 AM, wrichcirw wrote:
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:
I came across this exercise on the internet, and disagree quite a bit with the answer. I was hoping to get some thoughts on it. It can be found here: http://grockit.com...

Jacques will run for class president unless Mitzi runs for class president. Which of the following is/are IMPOSSIBLE? [Choose all that apply]

(i)-Jacques runs for class president unopposed.
(ii)-Mitzi runs for class president unopposed.
(iii)-Only Jacques and Mitzi run for class president.
(iv)-Eleanor runs for class president unopposed.
(v)-No one runs for class president.


My reasoning was that i and ii are both possible; Jacques and Mitzi running are two mutually exclusive events, so it's possible that either of them could run unopposed.

I also found iv and v fairly straight-forward: both are impossible. Iv is impossible because either Jacques or Mitzi are going to run, meaning that another person wouldn't be able to run unopposed. The same logic extends to V.

So far, everything I have reasoned is correct, according to the answer key. The controversy comes in with answer iii. It suggests that both Jacques and Mitzi will run. But how is this possible? Jacques and Mitzi running are two mutually exclusive events, are they not? "Jacques will run unless Mitzi runs" or X unless Y. In order words, if Y occurs, X cannot. How, then, is iii possible?

Any thoughts?

The underlined is the flaw in an otherwise well-reasoned explanation. X unless Y is the same as "if Y does NOT occur, X occurs", i.e. nY=>X

http://www.alphascore.com...

Contrapositive is nX=>Y.

Neither of these statements imply mutual exclusivity...there is no necessary condition as to what happens "if X" or "if Y", and so there is no statement of exclusion for either condition.

How does those statement not imply mutual exclusivity? If X, not Y. If Y, not X. They are clearly mutually exclusive.

Because those are not the statements relevant to the question. Please reread my explanation, especially the underlined. Pay attention to detail.

For me, the most convincing part of the link was the explanation that began "You can also look at Unless as essentially the same as saying "IF NOT""

Good luck on the LSAT.

Your explanation makes no sense whatsoever.

Then you should not be taking the LSAT.

The definition of mutually exclusive: Two events are mutually exclusive if they cannot occur at the same time. Jaques running for president and Mitizi running for president are mutually exclusive events, since if Mitizi runs, Jaques won't run. Q.E.D.
wrichcirw
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7/7/2014 4:47:29 PM
Posted: 2 years ago
At 7/7/2014 4:45:59 PM, dylancatlow wrote:
At 7/7/2014 4:37:23 PM, wrichcirw wrote:

The definition of mutually exclusive: Two events are mutually exclusive if they cannot occur at the same time. Jaques running for president and Mitizi running for president are mutually exclusive events, since if Mitizi runs, Jaques won't run. Q.E.D.

You're rephrasing the question...it's not a valid paraphrase. Read the link I provided, reread my explanation, think about it a bit, and tell me when you get it, because it is correct.
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
dylancatlow
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7/7/2014 4:51:58 PM
Posted: 2 years ago
At 7/7/2014 4:47:29 PM, wrichcirw wrote:
At 7/7/2014 4:45:59 PM, dylancatlow wrote:
At 7/7/2014 4:37:23 PM, wrichcirw wrote:

The definition of mutually exclusive: Two events are mutually exclusive if they cannot occur at the same time. Jaques running for president and Mitizi running for president are mutually exclusive events, since if Mitizi runs, Jaques won't run. Q.E.D.

You're rephrasing the question...it's not a valid paraphrase. Read the link I provided, reread my explanation, think about it a bit, and tell me when you get it, because it is correct.

Can you please rephrase your point?
dylancatlow
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7/7/2014 4:59:37 PM
Posted: 2 years ago
At 7/7/2014 4:55:55 AM, wrichcirw wrote:
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:

Neither of these statements imply mutual exclusivity...there is no necessary condition as to what happens "if X" or "if Y", and so there is no statement of exclusion for either condition.


How is a necessary to know what happens "If X" or "If Y" to know that X and Y are mutually exclusive?
wrichcirw
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7/7/2014 5:03:24 PM
Posted: 2 years ago
At 7/7/2014 4:59:37 PM, dylancatlow wrote:
At 7/7/2014 4:55:55 AM, wrichcirw wrote:
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:

Neither of these statements imply mutual exclusivity...there is no necessary condition as to what happens "if X" or "if Y", and so there is no statement of exclusion for either condition.


How is a necessary to know what happens "If X" or "If Y" to know that X and Y are mutually exclusive?

You have to know that "Given X, Not Y" or "Given Y, Not X" in order to have mutual exclusivity. But, if you look at the link, the way "unless" is phrased is equivalent to "IF NOT". So, the proper symbolic representation of the question is "Given NOT Y, then X". That's not a statement of mutual exclusivity...it says nothing about what happens given Y or given X, which means you can very well have the case where "given Y, X", or "given X, Y".
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
dylancatlow
Posts: 12,251
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7/7/2014 5:05:47 PM
Posted: 2 years ago
At 7/7/2014 5:03:24 PM, wrichcirw wrote:
At 7/7/2014 4:59:37 PM, dylancatlow wrote:
At 7/7/2014 4:55:55 AM, wrichcirw wrote:
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:

Neither of these statements imply mutual exclusivity...there is no necessary condition as to what happens "if X" or "if Y", and so there is no statement of exclusion for either condition.


How is a necessary to know what happens "If X" or "If Y" to know that X and Y are mutually exclusive?

You have to know that "Given X, Not Y" or "Given Y, Not X" in order to have mutual exclusivity. But, if you look at the link, the way "unless" is phrased is equivalent to "IF NOT". So, the proper symbolic representation of the question is "Given NOT Y, then X". That's not a statement of mutual exclusivity...it says nothing about what happens given Y or given X, which means you can very well have the case where "given Y, X", or "given X, Y".

Given that Mitzi runs, Jaques won't run.... Given that Jaques runs, Mitizi didn't run.
wrichcirw
Posts: 11,196
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7/7/2014 5:08:05 PM
Posted: 2 years ago
At 7/7/2014 5:05:47 PM, dylancatlow wrote:
At 7/7/2014 5:03:24 PM, wrichcirw wrote:
At 7/7/2014 4:59:37 PM, dylancatlow wrote:
At 7/7/2014 4:55:55 AM, wrichcirw wrote:
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:

Neither of these statements imply mutual exclusivity...there is no necessary condition as to what happens "if X" or "if Y", and so there is no statement of exclusion for either condition.


How is a necessary to know what happens "If X" or "If Y" to know that X and Y are mutually exclusive?

You have to know that "Given X, Not Y" or "Given Y, Not X" in order to have mutual exclusivity. But, if you look at the link, the way "unless" is phrased is equivalent to "IF NOT". So, the proper symbolic representation of the question is "Given NOT Y, then X". That's not a statement of mutual exclusivity...it says nothing about what happens given Y or given X, which means you can very well have the case where "given Y, X", or "given X, Y".

Given that Mitzi runs, Jaques won't run.... Given that Jaques runs, Mitizi didn't run.

Again, you're not phrasing the question properly. It's "Given Mitzi does NOT run, Jacques will run". That says nothing about what would happen if Mitzi runs.

As it is, you need to be able to work on a symbolic level if you want a decent score (160+) on the LSAT. It's all about speed.
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
dylancatlow
Posts: 12,251
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7/7/2014 5:16:15 PM
Posted: 2 years ago
At 7/7/2014 5:08:05 PM, wrichcirw wrote:
At 7/7/2014 5:05:47 PM, dylancatlow wrote:
At 7/7/2014 5:03:24 PM, wrichcirw wrote:
At 7/7/2014 4:59:37 PM, dylancatlow wrote:
At 7/7/2014 4:55:55 AM, wrichcirw wrote:
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:

Neither of these statements imply mutual exclusivity...there is no necessary condition as to what happens "if X" or "if Y", and so there is no statement of exclusion for either condition.


How is a necessary to know what happens "If X" or "If Y" to know that X and Y are mutually exclusive?

You have to know that "Given X, Not Y" or "Given Y, Not X" in order to have mutual exclusivity. But, if you look at the link, the way "unless" is phrased is equivalent to "IF NOT". So, the proper symbolic representation of the question is "Given NOT Y, then X". That's not a statement of mutual exclusivity...it says nothing about what happens given Y or given X, which means you can very well have the case where "given Y, X", or "given X, Y".

Given that Mitzi runs, Jaques won't run.... Given that Jaques runs, Mitizi didn't run.

Again, you're not phrasing the question properly. It's "Given Mitzi does NOT run, Jacques will run". That says nothing about what would happen if Mitzi runs.

That was your statement, not his. His was: 'Jacques will run unless Mitzi runs' or X unless Y. In order words, if Y occurs, X cannot. So if Mitzi runs, Jaques won't run.
wrichcirw
Posts: 11,196
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7/7/2014 5:17:27 PM
Posted: 2 years ago
At 7/7/2014 5:16:15 PM, dylancatlow wrote:
At 7/7/2014 5:08:05 PM, wrichcirw wrote:
At 7/7/2014 5:05:47 PM, dylancatlow wrote:
At 7/7/2014 5:03:24 PM, wrichcirw wrote:
At 7/7/2014 4:59:37 PM, dylancatlow wrote:
At 7/7/2014 4:55:55 AM, wrichcirw wrote:
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:

Neither of these statements imply mutual exclusivity...there is no necessary condition as to what happens "if X" or "if Y", and so there is no statement of exclusion for either condition.


How is a necessary to know what happens "If X" or "If Y" to know that X and Y are mutually exclusive?

You have to know that "Given X, Not Y" or "Given Y, Not X" in order to have mutual exclusivity. But, if you look at the link, the way "unless" is phrased is equivalent to "IF NOT". So, the proper symbolic representation of the question is "Given NOT Y, then X". That's not a statement of mutual exclusivity...it says nothing about what happens given Y or given X, which means you can very well have the case where "given Y, X", or "given X, Y".

Given that Mitzi runs, Jaques won't run.... Given that Jaques runs, Mitizi didn't run.

Again, you're not phrasing the question properly. It's "Given Mitzi does NOT run, Jacques will run". That says nothing about what would happen if Mitzi runs.

That was your statement, not his. His was: 'Jacques will run unless Mitzi runs' or X unless Y. In order words, if Y occurs, X cannot. So if Mitzi runs, Jaques won't run.

sigh...replace "unless" with IF NOT.

Then you get the statement "If Mitzi does NOT run, Jacques will run". Your symbology is all wrong.
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
dylancatlow
Posts: 12,251
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7/7/2014 5:21:15 PM
Posted: 2 years ago
At 7/7/2014 5:17:27 PM, wrichcirw wrote:
At 7/7/2014 5:16:15 PM, dylancatlow wrote:
At 7/7/2014 5:08:05 PM, wrichcirw wrote:
At 7/7/2014 5:05:47 PM, dylancatlow wrote:
At 7/7/2014 5:03:24 PM, wrichcirw wrote:
At 7/7/2014 4:59:37 PM, dylancatlow wrote:
At 7/7/2014 4:55:55 AM, wrichcirw wrote:
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:

Neither of these statements imply mutual exclusivity...there is no necessary condition as to what happens "if X" or "if Y", and so there is no statement of exclusion for either condition.


How is a necessary to know what happens "If X" or "If Y" to know that X and Y are mutually exclusive?

You have to know that "Given X, Not Y" or "Given Y, Not X" in order to have mutual exclusivity. But, if you look at the link, the way "unless" is phrased is equivalent to "IF NOT". So, the proper symbolic representation of the question is "Given NOT Y, then X". That's not a statement of mutual exclusivity...it says nothing about what happens given Y or given X, which means you can very well have the case where "given Y, X", or "given X, Y".

Given that Mitzi runs, Jaques won't run.... Given that Jaques runs, Mitizi didn't run.

Again, you're not phrasing the question properly. It's "Given Mitzi does NOT run, Jacques will run". That says nothing about what would happen if Mitzi runs.

That was your statement, not his. His was: 'Jacques will run unless Mitzi runs' or X unless Y. In order words, if Y occurs, X cannot. So if Mitzi runs, Jaques won't run.

sigh...replace "unless" with IF NOT.

Then you get the statement "If Mitzi does NOT run, Jacques will run". Your symbology is all wrong.

Those are not equivalent. The sentence "Jacques will run unless Mitzi runs" implies that if Mitzi runs, Jacques won't, while your sentence just implies that Jaques will run if Mitiiz doesn't (it doesn't mean Jaques won't run if Mitizi also runs).
wrichcirw
Posts: 11,196
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7/7/2014 5:22:00 PM
Posted: 2 years ago
At 7/7/2014 5:21:15 PM, dylancatlow wrote:
At 7/7/2014 5:17:27 PM, wrichcirw wrote:
At 7/7/2014 5:16:15 PM, dylancatlow wrote:
At 7/7/2014 5:08:05 PM, wrichcirw wrote:
At 7/7/2014 5:05:47 PM, dylancatlow wrote:
At 7/7/2014 5:03:24 PM, wrichcirw wrote:
At 7/7/2014 4:59:37 PM, dylancatlow wrote:
At 7/7/2014 4:55:55 AM, wrichcirw wrote:
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:

Neither of these statements imply mutual exclusivity...there is no necessary condition as to what happens "if X" or "if Y", and so there is no statement of exclusion for either condition.


How is a necessary to know what happens "If X" or "If Y" to know that X and Y are mutually exclusive?

You have to know that "Given X, Not Y" or "Given Y, Not X" in order to have mutual exclusivity. But, if you look at the link, the way "unless" is phrased is equivalent to "IF NOT". So, the proper symbolic representation of the question is "Given NOT Y, then X". That's not a statement of mutual exclusivity...it says nothing about what happens given Y or given X, which means you can very well have the case where "given Y, X", or "given X, Y".

Given that Mitzi runs, Jaques won't run.... Given that Jaques runs, Mitizi didn't run.

Again, you're not phrasing the question properly. It's "Given Mitzi does NOT run, Jacques will run". That says nothing about what would happen if Mitzi runs.

That was your statement, not his. His was: 'Jacques will run unless Mitzi runs' or X unless Y. In order words, if Y occurs, X cannot. So if Mitzi runs, Jaques won't run.

sigh...replace "unless" with IF NOT.

Then you get the statement "If Mitzi does NOT run, Jacques will run". Your symbology is all wrong.

Those are not equivalent. The sentence "Jacques will run unless Mitzi runs" implies that if Mitzi runs, Jacques won't, while your sentence just implies that Jaques will run if Mitiiz doesn't (it doesn't mean Jaques won't run if Mitizi also runs).

Reread the link I provided until you get it, or until you decide to stick to your own convoluted reasoning.
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
dylancatlow
Posts: 12,251
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7/7/2014 5:22:39 PM
Posted: 2 years ago
At 7/7/2014 5:22:00 PM, wrichcirw wrote:
At 7/7/2014 5:21:15 PM, dylancatlow wrote:
At 7/7/2014 5:17:27 PM, wrichcirw wrote:
At 7/7/2014 5:16:15 PM, dylancatlow wrote:
At 7/7/2014 5:08:05 PM, wrichcirw wrote:
At 7/7/2014 5:05:47 PM, dylancatlow wrote:
At 7/7/2014 5:03:24 PM, wrichcirw wrote:
At 7/7/2014 4:59:37 PM, dylancatlow wrote:
At 7/7/2014 4:55:55 AM, wrichcirw wrote:
At 7/1/2014 5:16:14 PM, JohnMaynardKeynes wrote:

Neither of these statements imply mutual exclusivity...there is no necessary condition as to what happens "if X" or "if Y", and so there is no statement of exclusion for either condition.


How is a necessary to know what happens "If X" or "If Y" to know that X and Y are mutually exclusive?

You have to know that "Given X, Not Y" or "Given Y, Not X" in order to have mutual exclusivity. But, if you look at the link, the way "unless" is phrased is equivalent to "IF NOT". So, the proper symbolic representation of the question is "Given NOT Y, then X". That's not a statement of mutual exclusivity...it says nothing about what happens given Y or given X, which means you can very well have the case where "given Y, X", or "given X, Y".

Given that Mitzi runs, Jaques won't run.... Given that Jaques runs, Mitizi didn't run.

Again, you're not phrasing the question properly. It's "Given Mitzi does NOT run, Jacques will run". That says nothing about what would happen if Mitzi runs.

That was your statement, not his. His was: 'Jacques will run unless Mitzi runs' or X unless Y. In order words, if Y occurs, X cannot. So if Mitzi runs, Jaques won't run.

sigh...replace "unless" with IF NOT.

Then you get the statement "If Mitzi does NOT run, Jacques will run". Your symbology is all wrong.

Those are not equivalent. The sentence "Jacques will run unless Mitzi runs" implies that if Mitzi runs, Jacques won't, while your sentence just implies that Jaques will run if Mitiiz doesn't (it doesn't mean Jaques won't run if Mitizi also runs).

Reread the link I provided until you get it, or until you decide to stick to your own convoluted reasoning.

Okay, crazy.
wrichcirw
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7/7/2014 5:23:17 PM
Posted: 2 years ago
At 7/7/2014 5:22:39 PM, dylancatlow wrote:
At 7/7/2014 5:22:00 PM, wrichcirw wrote:

Reread the link I provided until you get it, or until you decide to stick to your own convoluted reasoning.

Okay, crazy.

I'm not the one insisting that the wrong answer is correct.
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
dylancatlow
Posts: 12,251
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7/7/2014 5:25:51 PM
Posted: 2 years ago
At 7/7/2014 5:23:17 PM, wrichcirw wrote:
At 7/7/2014 5:22:39 PM, dylancatlow wrote:
At 7/7/2014 5:22:00 PM, wrichcirw wrote:

Reread the link I provided until you get it, or until you decide to stick to your own convoluted reasoning.

Okay, crazy.

I'm not the one insisting that the wrong answer is correct.

Why, sure you aren't ; - )