## If and only if

Prepare for the LSAT or discuss it with others in this forum.
mhisha

Posts: 1
Joined: Thu Nov 03, 2011 2:06 am

### If and only if

Hi all,

Can anybody please help with the IF AND ONLY IF construction? Say, A if and only if B, leads to 1) A if B and 2) A only if B

Therefore: 1) implies if B then A ( B=>A)
and 2) implies only if B then A (A=>B)

Am i correct in understanding it?

QUESTION : IS A<=>B equal to B<=>A ?

Best,
M

barneytrouble

Posts: 239
Joined: Wed Aug 17, 2011 11:43 pm

### Re: If and only if

mhisha wrote:Hi all,

Can anybody please help with the IF AND ONLY IF construction? Say, A if and only if B, leads to 1) A if B and 2) A only if B

Therefore: 1) implies if B then A ( B=>A)
and 2) implies only if B then A (A=>B)

Am i correct in understanding it?

QUESTION : IS A<=>B equal to B<=>A ?

Best,
M

"A if and only if B" means that either A and B both happen, or neither one of them does.

noleknight16

Posts: 940
Joined: Thu Dec 02, 2010 3:09 am

### Re: If and only if

A if and only if B

A====>B
-B====>-A

AND

B====>A
-A====>-B

Hope that helps

GirlStop

Posts: 126
Joined: Tue Oct 25, 2011 9:49 am

### Re: If and only if

I believe Nole is right.

PowerScore diagram's it as a<--->b to show it goes both ways

ColtsFan88

Posts: 1431
Joined: Thu Oct 13, 2011 5:05 pm

### Re: If and only if

A<->B is equal to B<->A.

homestyle28

Posts: 2362
Joined: Thu Jun 04, 2009 12:48 pm

### Re: If and only if

just to get crazy up in here:
Yeah A if and only if B = A->B and B->A, ~B->~A and ~A->~B, ~A v B and ~B v A

all are those sentences are truth functionally equivalent

SanDiegoJake

Posts: 149
Joined: Mon Mar 07, 2011 3:17 pm

### Re: If and only if

Everyone who has posted is right. "If and Only If" means it goes both ways. Use the double arrow, or two separate diagrams, whichever works best for you. The only thing I have to add is "If but Only If" works the exact same way.

Good luck.