Analytical Reasoning Condition Reversal

TulipMelody
Posts: 13
Joined: Thu Sep 13, 2012 1:58 am

Analytical Reasoning Condition Reversal

Postby TulipMelody » Thu May 09, 2013 12:18 am

Hi, I really need some clerification for this type of conditions:

"If A goes to Italy, B will go, too."

With this condition, can I infer that if B goes to Italy, A alreay goes, too? A -> B, so B -> A

Another similiar example:

"N cannot sing unless M sings." M-> N. Can I infer that if N is singing, M is also/already singing?


Basically, I wonder if the reverse of these conditons are valid. I have this struggle because both use the reverse or not use the reverse make sense to me...

Thank you~

User avatar
90convoy
Posts: 918
Joined: Thu Jul 05, 2012 8:59 pm

Re: Analytical Reasoning Condition Reversal

Postby 90convoy » Thu May 09, 2013 12:28 am

TulipMelody wrote:Hi, I really need some clerification for this type of conditions:

"If A goes to Italy, B will go, too."

With this condition, can I infer that if B goes to Italy, A alreay goes, too? A -> B, so B -> A

Another similiar example:

"N cannot sing unless M sings." M-> N. Can I infer that if N is singing, M is also/already singing?


Basically, I wonder if the reverse of these conditons are valid. I have this struggle because both use the reverse or not use the reverse make sense to me...

Thank you~


I believe for the first one you can't assume that A already goes if B goes and for the second one YES if N is singing then M has to be singing. The only way that N can sing is if M sings so if N is singing then so M.

Daily_Double
Posts: 1035
Joined: Tue Dec 04, 2012 8:45 pm

Re: Analytical Reasoning Condition Reversal

Postby Daily_Double » Thu May 09, 2013 12:50 am

TulipMelody wrote:Hi, I really need some clerification for this type of conditions:

"If A goes to Italy, B will go, too."

With this condition, can I infer that if B goes to Italy, A alreay goes, too? A -> B, so B -> A

No. With this statement you can infer two things:

1. When A goes to Italy, B always goes to Italy, and
2. When B does not go to Italy, A does not go to Italy

Another similiar example:

TulipMelody wrote:"N cannot sing unless M sings." M-> N. Can I infer that if N is singing, M is also/already singing?


The answer to your question is yes, but your justification is off. You represented the relationship falsely. Once again, two things here. The phrases "unless, until, without, except," create a unique relationship which is represented by using the phrase above, and what it refers to, as the necessary condition, and negating the sufficient condition. Or you could simply take the condition that the phrase above refers to, negate it, and make that the sufficient condition then make the other one the necessary condition. Either way. Because I'm used to doing it the first way, I'll explain it that way:

You can infer:
1. If N sings then M sings
2. If M does not sing, then N does not sing

TulipMelody wrote:Basically, I wonder if the reverse of these conditons are valid. I have this struggle because both use the reverse or not use the reverse make sense to me...

Thank you~


Short answer, not no, but God no. The thing is that this is the most basic of all logic. I don't know what book your using, but I know that you aren't far enough in it. Keep at it. Read articles online about conditional logic and know the relationships in and out. Eventually you won't have to diagram it, eventually you will hear conditional relationships and mentally diagram them, eventually, you won't even have to think about it. When you hear a friend of yours taking the absence of a sufficient condition to prove the absence of a necessary condition or the presence of a necessary condition as proof for the presence of the sufficient condition and you will recognize it, remember I called it first. But you've got a long way to go. Read the articles here, buy the books, buy the cambridge packets, do work.
Last edited by Daily_Double on Thu May 09, 2013 12:59 am, edited 1 time in total.

User avatar
Clearly
Posts: 4165
Joined: Sat Feb 11, 2012 4:09 pm

Re: Analytical Reasoning Condition Reversal

Postby Clearly » Thu May 09, 2013 12:50 am

Alright, I'm exhausted but I'll try to get you on track with these.
"If A goes to Italy, B will go, too."
With this condition, can I infer that if B goes to Italy, A alreay goes, too? A -> B, so B -> A

No, you can not. This can only be interpreted as A->B and it's contrapositive, ~B->~A
It's entirely possible that B can go without A going, all we know is that if A goes, B must go.
What you have done is called affirming the consequent, or the converse flaw, basically a mistaken reversal, it's no good.

"N cannot sing unless M sings." M-> N. Can I infer that if N is singing, M is also/already singing?
You have this diagrammed incorrectly. It's invalid. This is symbolized if N->M and its contrapositive ~M->~N
You have again affirmed the consequent, or incorrectly reversed the statement. Your applying the same flaw as above to the already mistakenly reversed diagram actually netted you the correct inference this time. If N is singing, M must indeed be singing.

I'd recommend picking up a guide to LR if you are struggling with conditional logic, as it takes practice and its not entirely easy to figure out on your own. Dealing with only if, if and only if, unless, etc needs practice. Also, getting good at what inferences you can make properly from a statement needs to be taught. Get used to the idea that whatever ends up on the right side of the arrow (the necessary) never tells you anything about anything (unless its the sufficient in another rule)... Sure in this case if M is singing N might be singing, but he also might not be. Just because you have an effect doesn't mean you can backtrack to that cause. An infinite number of other things may have caused M to sing besides N singing.

Keep studying and practicing, and do pick up a book if you haven't already. Manhattan's is pretty good, although they all pretty clearly explain this stuff.

User avatar
Clearly
Posts: 4165
Joined: Sat Feb 11, 2012 4:09 pm

Re: Analytical Reasoning Condition Reversal

Postby Clearly » Thu May 09, 2013 12:52 am

Daily_Double wrote:
With this condition, can I infer that if B goes to Italy, A alreay goes, too? A -> B, so B -> A
No. With this statement you can infer two things:

1. When B goes to Italy, A always goes to Italy, and
2. When A does not go to Italy, B does not go to Italy



I'm afraid you have this backwards.

Daily_Double
Posts: 1035
Joined: Tue Dec 04, 2012 8:45 pm

Re: Analytical Reasoning Condition Reversal

Postby Daily_Double » Thu May 09, 2013 12:57 am

Clearlynotstefan wrote:
Daily_Double wrote:
With this condition, can I infer that if B goes to Italy, A alreay goes, too? A -> B, so B -> A
No. With this statement you can infer two things:

1. When B goes to Italy, A always goes to Italy, and
2. When A does not go to Italy, B does not go to Italy



I'm afraid you have this backwards.


I deserve to be made fun of for this. I read the second half of his statement and the reversal part, that being said, not reading a question completely is something I'm embarrassed to have been caught doing.

User avatar
Clearly
Posts: 4165
Joined: Sat Feb 11, 2012 4:09 pm

Re: Analytical Reasoning Condition Reversal

Postby Clearly » Thu May 09, 2013 12:59 am

Daily_Double wrote:
Clearlynotstefan wrote:
Daily_Double wrote:
With this condition, can I infer that if B goes to Italy, A alreay goes, too? A -> B, so B -> A
No. With this statement you can infer two things:

1. When B goes to Italy, A always goes to Italy, and
2. When A does not go to Italy, B does not go to Italy



I'm afraid you have this backwards.


I deserve to be made fun of for this.



Haha, don't sweat it, happens to all of us! You nailed the explanation anyway, just mixed it up when writing it.

TulipMelody
Posts: 13
Joined: Thu Sep 13, 2012 1:58 am

Re: Analytical Reasoning Condition Reversal

Postby TulipMelody » Thu May 09, 2013 3:49 am

Clearlynotstefan wrote:Alright, I'm exhausted but I'll try to get you on track with these.
"If A goes to Italy, B will go, too." .


I didn't mean to exhaust anyone other than myself, LOL. First, thank you very much for the patient explanation. I really appreciate all your input.

I actually have been studying from a couple of books, which varies from the LSAC publications to other test-prep books. Some of them indeed provided the same explanations as yours. I couldn't understand the books because my "false reversal method" actually got me the right answers half of the time (I think I now know why). I finally decided to come up here and ask people for help, embarrass myself along the way just for fun, lol~

Since both the books and colleagues explain the same, I need to rewire my brain. In order to do that, I need to work out the correct logic and make sense of it first. If you don’t mind, can you take a look at my baby steps?

“If A goes to Italy, B will go, too.”

1) A goes, then B goes

A’s action (“going”) directly affects, or leads to, B’s action (“going”). Just like, if it rains, we pull out umbrellas – fact #1 leads to fact #2.

2) B goes, then A could go and could not go

Nobody said anything about B’s action (“going”) and its effects. Therefore, I cannot assume any actions (“going” or “not going”) from anybody (A, in this case) as a result of B’s action (“going”). A has freedom.

3) A does not go, then B could go or could not go

Same, nobody said anything about A’s “not going” and its effects.

4) B does not go, then A does not go

Okay, this is where you and the books got me. The only way I can explain to myself is that, the opposite scenario (“B does not go, then A goes”) is an invalid scenario. Therefore, ~B --> ~A is the only one left.

What do you think? Did I get 2) and 3) right?

And whenever there is an “if” in questions like this, there is always a linear relationship. What I mean by “linear” is that something leads to something else, like a cause-and-effect relationship? Am I on the right track?

Thank you again. :D

User avatar
Clearly
Posts: 4165
Joined: Sat Feb 11, 2012 4:09 pm

Re: Analytical Reasoning Condition Reversal

Postby Clearly » Thu May 09, 2013 4:11 am

TulipMelody wrote:
Clearlynotstefan wrote:Alright, I'm exhausted but I'll try to get you on track with these.
"If A goes to Italy, B will go, too." .


I didn't mean to exhaust anyone other than myself, LOL. First, thank you very much for the patient explanation. I really appreciate all your input.

I actually have been studying from a couple of books, which varies from the LSAC publications to other test-prep books. Some of them indeed provided the same explanations as yours. I couldn't understand the books because my "false reversal method" actually got me the right answers half of the time (I think I now know why). I finally decided to come up here and ask people for help, embarrass myself along the way just for fun, lol~

Since both the books and colleagues explain the same, I need to rewire my brain. In order to do that, I need to work out the correct logic and make sense of it first. If you don’t mind, can you take a look at my baby steps?

“If A goes to Italy, B will go, too.”

1) A goes, then B goes

A’s action (“going”) directly affects, or leads to, B’s action (“going”). Just like, if it rains, we pull out umbrellas – fact #1 leads to fact #2.

2) B goes, then A could go and could not go

Nobody said anything about B’s action (“going”) and its effects. Therefore, I cannot assume any actions (“going” or “not going”) from anybody (A, in this case) as a result of B’s action (“going”). A has freedom.

3) A does not go, then B could go or could not go

Same, nobody said anything about A’s “not going” and its effects.

4) B does not go, then A does not go

Okay, this is where you and the books got me. The only way I can explain to myself is that, the opposite scenario (“B does not go, then A goes”) is an invalid scenario. Therefore, ~B --> ~A is the only one left.

What do you think? Did I get 2) and 3) right?

And whenever there is an “if” in questions like this, there is always a linear relationship. What I mean by “linear” is that something leads to something else, like a cause-and-effect relationship? Am I on the right track?

Thank you again. :D


You just absolutely crushed it, and hit pretty much every important point about straight forward if then statements. The big one being that the necessary condition on the right, doesn't have any bearing to the condition on the left, that is basically to say we use an arrow for a reason, and you can't work backwards from that. Awesome. Good job man!

The inverse way of looking at the statements is called a contrapositive. Every single if-then statement has a contrapositive, even those including and, or, nor etc.

The contrapositive is useful because its basically just a way of rewording the original statement, but it gives you a new sufficient condition, that is to say, it basically gives you a new cause (following from basically the opposite form of the original statement)

To form a contrapositive, you simple flip the original statement around, and negate the terms. If it included the words and/or, you simply exchange them, basically and becomes or, and or becomes and...It seems weird now, but after you see enough of them to get comfortable with it, you will see why it works that way.

So lets take a look at a few conditionals and the contrapositives

If you are in NY, then you are in the USA
NY->USA
This is a conditional statement, and it happens to be true. So we know what if you are in the USA? Thats right, absolutely nothing, you could be in NY sure, but you could also be in Montana, we just don't know. But think of this! Can you NOT be in the USA and still be in NY? Of course not, because we already know that NY->USA. This is the contrapositive.
By negating, and flipping the terms, we get
~USA->~NY

Basically you end up in a feedback loop of sorts. Can you be not in the USA and be in NY, no because if your in NY, you have to be in the USA, and if you're not in the USA you can't be in NY, because if you were in NY...etc.

Lets spice it up a bit now

If you're on TLS then you're informed, or not paying attention.

TLS->Inf or ~Pay Att

Contrapositive would be

Pay attention AND ~informed ->~on TLS

If you think about it, negating and flipping and switching or to and makes perfect sense. Either of those things but at least one results from being on TLS, based on this in order for us to prove someone isn't on TLS we would have to prove NEITHER of the known causes happened, because just one would still leave the door open to the other happening and thus they could still be on TLS, this is why and turns to or and or turns to and.


If you have any questions be sure to post them here, I'll check and try to answer them whenever I have time, just as people did for me when I was learning this stuff.

TulipMelody
Posts: 13
Joined: Thu Sep 13, 2012 1:58 am

Re: Analytical Reasoning Condition Reversal

Postby TulipMelody » Thu May 09, 2013 4:16 am

Clearlynotstefan wrote:"N cannot sing unless M sings." M-> N. Can I infer that if N is singing, M is also/already singing?
You have this diagrammed incorrectly. It's invalid. This is symbolized if N->M and its contrapositive ~M->~N
You have again affirmed the consequent, or incorrectly reversed the statement. Your applying the same flaw as above to the already mistakenly reversed diagram actually netted you the correct inference this time. If N is singing, M must indeed be singing.


Yep, you were right! The answer might be correct, yet I took the incorrect route. I need to fix it. Let me see..

"N cannot sing unless M sings," then:

1) M sings, then N sings
2) M does not sing, then N does not sing
3) N sings, then M sings
4) N does not sing, M does not sing

Differed from the earlier "A and B" example, M has stronger influence on N here. Either M sings or does not sing both have some effects on N. In the earlier example, A only have one effect on B, and that effect happens only when A goes to Italy. These different outcomes are created by the different wording of the statements. Am I on the right track?

Thank you~

User avatar
Clearly
Posts: 4165
Joined: Sat Feb 11, 2012 4:09 pm

Re: Analytical Reasoning Condition Reversal

Postby Clearly » Thu May 09, 2013 4:21 am

TulipMelody wrote:
Clearlynotstefan wrote:"N cannot sing unless M sings." M-> N. Can I infer that if N is singing, M is also/already singing?
You have this diagrammed incorrectly. It's invalid. This is symbolized if N->M and its contrapositive ~M->~N
You have again affirmed the consequent, or incorrectly reversed the statement. Your applying the same flaw as above to the already mistakenly reversed diagram actually netted you the correct inference this time. If N is singing, M must indeed be singing.


Yep, you were right! The answer might be correct, yet I took the incorrect route. I need to fix it. Let me see..

"N cannot sing unless M sings," then:

1) M sings, then N sings
2) M does not sing, then N does not sing
3) N sings, then M sings
4) N does not sing, M does not sing

Differed from the earlier "A and B" example, M has stronger influence on N here. Either M sings or does not sing both have some effects on N. In the earlier example, A only have one effect on B, and that effect happens only when A goes to Italy. These different outcomes are created by the different wording of the statements. Am I on the right track?

Thank you~


Eh, you're actually getting thrown off by the unless, and treating it like an "if and only if" (don't worry about that one yet).

The only two inferences valid inference from the above are
N->M
~M->~N

The original statement and it's contrapositive as explained above. Don't let the unless convince you that its a two way street, it's still a one way arrow, the guy on the right has just as much bearing on the guy on the left as he did in our Italy example. M happening doesn't tell us anything, N could still happen or not happen; and N not happening doesn't tell us anything, M could still go or not go. Basically unless statements will translate to a typical A->B format, and you can yield the contra and nothing else like always.

TulipMelody
Posts: 13
Joined: Thu Sep 13, 2012 1:58 am

Re: Analytical Reasoning Condition Reversal

Postby TulipMelody » Thu May 09, 2013 4:35 am

Clearlynotstefan wrote:
TulipMelody wrote:
Clearlynotstefan wrote:Alright, I'm exhausted but I'll try to get you on track with these.
"If A goes to Italy, B will go, too." .



Lets spice it up a bit now

If you're on TLS then you're informed, or not paying attention.

TLS->Inf or ~Pay Att

Contrapositive would be

Pay attention AND ~informed ->~on TLS

If you think about it, negating and flipping and switching or to and makes perfect sense. Either of those things but at least one results from being on TLS, based on this in order for us to prove someone isn't on TLS we would have to prove NEITHER of the known causes happened, because just one would still leave the door open to the other happening and thus they could still be on TLS, this is why and turns to or and or turns to and.


If you have any questions be sure to post them here, I'll check and try to answer them whenever I have time, just as people did for me when I was learning this stuff.


This is awesome! Both the NYC and TLS examples are so easy to absorb! This is so clear to me now. I agree that I need to do more practice, but this time with the correct logic..

Thank you so much!!!!!!!!!!!!!!!!!!!!!!!!!! It was like a thousand-dollar LSAT class right there!

TulipMelody
Posts: 13
Joined: Thu Sep 13, 2012 1:58 am

Re: Analytical Reasoning Condition Reversal

Postby TulipMelody » Thu May 09, 2013 4:38 am

Clearlynotstefan wrote:
TulipMelody wrote:
Clearlynotstefan wrote:"N cannot sing unless M sings." M-> N. Can I infer that if N is singing, M is also/already singing?
You have this diagrammed incorrectly. It's invalid. This is symbolized if N->M and its contrapositive ~M->~N


Eh, you're actually getting thrown off by the unless, and treating it like an "if and only if" (don't worry about that one yet).

The only two inferences valid inference from the above are
N->M
~M->~N

The original statement and it's contrapositive as explained above. Don't let the unless convince you that its a two way street, it's still a one way arrow, the guy on the right has just as much bearing on the guy on the left as he did in our Italy example. M happening doesn't tell us anything, N could still happen or not happen; and N not happening doesn't tell us anything, M could still go or not go. Basically unless statements will translate to a typical A->B format, and you can yield the contra and nothing else like always.


Thank you very much for this feedback, too. Yet, I think I need to come back for this tomorrow. My brain is not working now...lol!

Again, thank you so much to be around and help us!!!!!

User avatar
Clearly
Posts: 4165
Joined: Sat Feb 11, 2012 4:09 pm

Re: Analytical Reasoning Condition Reversal

Postby Clearly » Thu May 09, 2013 4:47 am

No problem! TLS can be a great resource and I'm glad to give back after getting a ton of help here myself. It's going to take some practice to get the hang of the different ways the LSAT sets up these conditional statements, I'll get you started with a few of the more common ones

If A then B
A->B
~B -> ~A

A only if B
A -> B
~B -> ~A

A if and only if B
This is a tricky one, this is the rare case where they both cause each other
A<->B
~A<->~B

X unless Y
IF not X then Y
IF not Y then X

If A then B and C
A->B+C
~C OR ~B ->~A

If A then B or C
A->B or C
~B and ~C -> ~A

These are by far the most common set ups for conditional statements on LG at least, and getting to know them and how to form a contrapositive quickly makes quick work of games that rely on these rules. Keep it up, and post any questions you have. Remember to not to take it too far! You can never work backwards from the arrow!

TulipMelody
Posts: 13
Joined: Thu Sep 13, 2012 1:58 am

Re: Analytical Reasoning Condition Reversal

Postby TulipMelody » Fri May 10, 2013 1:14 am

Clearlynotstefan wrote:
TulipMelody wrote:
Clearlynotstefan wrote:Eh, you're actually getting thrown off by the unless, and treating it like an "if and only if" (don't worry about that one yet).

The only two inferences valid inference from the above are
N->M
~M->~N

The original statement and it's contrapositive as explained above. Don't let the unless convince you that its a two way street, it's still a one way arrow, the guy on the right has just as much bearing on the guy on the left as he did in our Italy example. M happening doesn't tell us anything, N could still happen or not happen; and N not happening doesn't tell us anything, M could still go or not go. Basically unless statements will translate to a typical A->B format, and you can yield the contra and nothing else like always.


Yes, I agree with the contrapositive part. Yeah...after thinking about it, it's true that if M sings, N could sing and could not sing. I see! How interesting! I'm gonna get more practice on these types.

Thank you!

TulipMelody
Posts: 13
Joined: Thu Sep 13, 2012 1:58 am

Re: Analytical Reasoning Condition Reversal

Postby TulipMelody » Fri May 10, 2013 1:19 am

Clearlynotstefan wrote:No problem! TLS can be a great resource and I'm glad to give back after getting a ton of help here myself. It's going to take some practice to get the hang of the different ways the LSAT sets up these conditional statements, I'll get you started with a few of the more common ones

If A then B
A->B
~B -> ~A

A only if B
A -> B
~B -> ~A

A if and only if B
This is a tricky one, this is the rare case where they both cause each other
A<->B
~A<->~B

X unless Y
IF not X then Y
IF not Y then X

If A then B and C
A->B+C
~C OR ~B ->~A

If A then B or C
A->B or C
~B and ~C -> ~A

These are by far the most common set ups for conditional statements on LG at least, and getting to know them and how to form a contrapositive quickly makes quick work of games that rely on these rules. Keep it up, and post any questions you have. Remember to not to take it too far! You can never work backwards from the arrow!


Great notes!!! Thank you. I am going to study a little more into the "only if" and "if and only if" once I see the actual quesiton. Moments like this, I wonder, "have I been using English incorrectly the whole time?" LOL!

Well, fun experience!

Thank you for sharing!!!




Return to “LSAT Prep and Discussion Forum”

Who is online

Users browsing this forum: PantoroB and 8 guests