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

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

Borek
Mentor
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.

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

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.