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

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?

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

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!?

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

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.

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