What does this mean? Whats the difference between IFF and IF?

[BloodyFrozen]

What does this mean? Whats the difference between IFF and IF?

 

[Borek]

http://en.wikipedia.org/wiki/If_and_only_if

 

[mathman]

What does this mean? Whats the difference between IFF and IF?

Logical implication A -> B can be expressed as if A then B.

A -> B and B -> A can be expressed as iff A then B.

 

[BloodyFrozen]

Logical implication A -> B can be expressed as if A then B.

A -> B and B -> A can be expressed as iff A then B.

Oh, I see now.

A<->B is iff

and A->B is if

 

[SteveL27]

Oh, I see now.

A<->B is iff

and A->B is if

Another way to think about it is that $A \Leftrightarrow B$ means that $A$ and $B$ have the same truth value. Either both are true or both are false.

If you are asked to do a proof of an IFF statement, you should break it down into two proofs: one of $A \Rightarrow B$ and the other of $B \Rightarrow A$. Typically one direction will be easier than the other.