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

1. Jun 24, 2011

### BloodyFrozen

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

2. Jun 24, 2011

### Staff: Mentor

3. Jun 25, 2011

### mathman

Re: Iff

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.

4. Jun 25, 2011

### BloodyFrozen

Re: Iff

Oh, I see now.

A<->B is iff

and A->B is if

5. Jun 25, 2011

### SteveL27

Re: Iff

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.