If and only if Forum

[mhisha]

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

[barneytrouble]

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]

A if and only if B

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

AND

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


Hope that helps

[GirlStop]

I believe Nole is right.

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

[ColtsFan88]

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

[homestyle28]

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]

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.