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 ?
Please help. I am confused about this? Thanks in advance.
Best,
M
If and only if

 Posts: 241
 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 ?
Please help. I am confused about this? Thanks in advance.
Best,
M
"A if and only if B" means that either A and B both happen, or neither one of them does.
 noleknight16
 Posts: 943
 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
A====>B
B====>A
AND
B====>A
A====>B
Hope that helps
 GirlStop
 Posts: 127
 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
PowerScore diagram's it as a<>b to show it goes both ways
 ColtsFan88
 Posts: 1432
 Joined: Thu Oct 13, 2011 5:05 pm
Re: If and only if
A<>B is equal to B<>A.
 homestyle28
 Posts: 2319
 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
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

 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.
Good luck.
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