If and only if

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mhisha

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If and only if

Postby mhisha » Thu Nov 03, 2011 2:16 am

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

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Joined: Wed Aug 17, 2011 11:43 pm

Re: If and only if

Postby barneytrouble » Thu Nov 03, 2011 2:49 am

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.

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noleknight16

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Re: If and only if

Postby noleknight16 » Thu Nov 03, 2011 5:06 am

A if and only if B

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

AND

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


Hope that helps :)

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GirlStop

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Re: If and only if

Postby GirlStop » Thu Nov 03, 2011 10:22 am

I believe Nole is right.

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

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ColtsFan88

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Re: If and only if

Postby ColtsFan88 » Thu Nov 03, 2011 10:42 am

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

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homestyle28

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Re: If and only if

Postby homestyle28 » Thu Nov 03, 2011 10:49 am

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

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Re: If and only if

Postby SanDiegoJake » Thu Nov 10, 2011 5:51 pm

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.



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