# Implication and Iff

The Symbols are and

## Implication:

Implication says "if ... then"

### Example:

If both a and b are odd numbers then (a+b) is even

can be written as:

both a and b are odd numbers (a+b) is even

The reason it points to the right is that it might not be true the other way

### Example:

Just because (a+b) is even does not mean that a and b are odd (they may both be even)

## Iff:

Iff says "if and only if"

It is an implication that goes **both ways**.

### Example:

x + y = 3 x = 3 − y

That one is true both ways!

### Example:

**a** and **b** are both integers.

If one of **a** and **b** is odd and the other is even then (**a+b**) is odd can be written as:

One of **a** and **b** is odd and the other is even (**a+b**) is odd

In this case it goes both ways, because if (**a+b**) is odd and **a** and **b** are both integers, then one of them must be odd and the other even.