Logic

Expert replies

oldheaven: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sun Jul 31, 2011 2:24 pm

by oldheaven » Sat Oct 01, 2011 4:05 am

"If A then B", now which of the following conclusion will not be true?

a) If A isn't true then B won't be true.
b) If B isn't true then A won't be true.
c) A isn't true or B isn't true.
d) If B isn't true A will be true.

Like this post

Source: Beat The GMAT — Critical Reasoning | Sat Oct 01, 2011 4:05 am

rishimaharaj: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Mon May 02, 2011 11:18 amFollowed by: 7 members; Location: Florida; Thanked: 20 times; GMAT Score:710

by rishimaharaj » Sat Oct 01, 2011 6:04 am

Hello Oldheaven,
Welcome to the site!

If you're having some problems with logic, I'd recommend you check out the Tashzila Logic Videos by Ankur Suryavanshi -- https://takshzilabeta.com/2010/10/21/logic-videos/.

Let A represent when A happens; Let B represent when B happens.
Let A' represent when A does not happen; Let B' represent when B does not happen.

According to the videos, Ankur explains that:
IF A, THEN B,
A -> B = Logical Necessity (LN)
B -> A = Logical Possibility (LP)
A' -> B' = Logical Possibility (LP)
B' -> A' = Logical Necessity (LN)

LN-
Whenever A happens, B will definitely happen.
Whenever B does not happen, A will definitely not have happened (because if A happened, B would have happened).

LP-
If be is happening, it is possible that A also happened, but B could have been caused by something else.
If A does not happen, it is possible that B also does not happen, but again, B could have been caused by something else.

Knowing this, we can see that:
a) If A isn't true then B won't be true. Possible, not not necessarily true.
b) If B isn't true then A won't be true. Definitely true.
c) A isn't true or B isn't true. This makes no sense; it doesn't state anything...
d) If B isn't true A will be true. This is not true: B' -> A' = LN.

The answer would be answer choice D.

To make more questions out of this one, try to come up with the LN/LP for the following statements:
1. Only If A, then B.
2. If and only if A, then B.

Hope this helps && Have fun!!
--Rishi

Last edited by rishimaharaj on Sat Oct 01, 2011 2:58 pm, edited 1 time in total.

Like this post

oldheaven: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sun Jul 31, 2011 2:24 pm

by oldheaven » Sat Oct 01, 2011 6:35 am

Hi,

Thank you rishimaharaj.
I saw in a book in which stated that in the third option ( A isn't true or B isn't true) we have (~A v(or) ~B) so we can conclude that (A -> ~B) which is absolutely wrong so decided to choose option #3.

what is your opinion about that?

Like this post

rishimaharaj: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Mon May 02, 2011 11:18 amFollowed by: 7 members; Location: Florida; Thanked: 20 times; GMAT Score:710

by rishimaharaj » Sat Oct 01, 2011 9:33 am

Hi Oldheaven,
I guess, now that you mention it, it makes a little more sense...
I think it is saying that either one or the other isn't happening. I think these are the following cases of this statement:
A' & B
A & B'
A' & B'

If this is the case, sometimes it is possible according to our statement (when B' -> A'), and sometimes it is not possible according to our statement (with A' & B and with A & B').

I guess this means that C is possibly true.

In the book that you were referring to, what does the "~" symbol mean in words?

--Rishi

Like this post

oldheaven: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sun Jul 31, 2011 2:24 pm

by oldheaven » Sat Oct 01, 2011 12:38 pm

Hi rishimaharaj

"~B" means " B does not happen ". (I thought this symbol is international,sorry).

The option C states that A'orB' (disjunction) which according to logical law can be interpreted as (A->B' , B->A').

1) A->B' , it is not possible.
2) B->A' , it's possible.

I'm somehow confused how a proposition (A->B (1)) can be true while the reversal of it (B'->A'(2)) is not true!?

Like this post

rishimaharaj: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Mon May 02, 2011 11:18 amFollowed by: 7 members; Location: Florida; Thanked: 20 times; GMAT Score:710

by rishimaharaj » Sat Oct 01, 2011 2:57 pm

Hello Oldheaven,

Have you checked out the Takshila Beta video I posted a link to earlier? The third and fourth videos on the page deal exclusively with conditionals and other tricky / possibly confusing situations.

Where did you hear/read this:

(A->B (1)) can be true while the reversal of it (B'->A'(2)) is not true

??

From my understanding, IF A, THEN B will always mean these two things at the same time:
1. A -> B (if A happens, B will definitely happen)
and
2. B' -> A' (if B does not happen, A will definitely not have happened)

One way for B' -> A' to not hold is if the statement was: Only if A, then B.
In this case,
A -> B = Logical Possibility (LP) (If A, possibly B happens. Not every time A happens B will happen).
B -> A = Logical Necessity (LN) (If B happens then A must have happened, because B can only happen when A happens).
A' -> B' = Logical Necessity (LN) (If A doesn't happen, then B can't have happened, because B can only happen whenever A happens).
B' -> A' = Logical Possibility (LP) (If B doesn't happen, it is possible that A hasn't happened. But it could be the case that A has happened and B has not happened.).

Does this help clarify anything at all?
Hehehe

--Rishi

Like this post

oldheaven: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sun Jul 31, 2011 2:24 pm

by oldheaven » Sun Oct 02, 2011 5:22 am

Hi again my dear buddy,

I have just seen the video and appreciated very much.
your instructions really helped me.

Now I have a conclusion which I have been confused on and I was wrong about it.Only can we write B'=>A' when we know that A=>B is true,am I right?

P.S. How many videos are there in this site about logic?

thank you.

Like this post

rishimaharaj: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Mon May 02, 2011 11:18 amFollowed by: 7 members; Location: Florida; Thanked: 20 times; GMAT Score:710

by rishimaharaj » Sun Oct 02, 2011 6:19 am

Hell Oldheaven

I think you are right, but I would also like feedback from any others who have been following this thread.

My thought process:
If A, then B = both A->B and B'->A' are true.
Only if A, then B = neither A->B nor B'->A' are true.
If and only if A, then B = both A->B and B'->A' are true (along with the B->A and A'->B').

In these three scenarios, if A->B is true, B'->A' is also true.
I don't know if there are any other scenarios to consider and/or whether or not we need to worry about it for the GMAT, though.

Hope this helps!
--Rishi

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review