Mutually Exclusive Sets are two sets that share NOTHING in common.

Example

Imagine we have the two sets below. Recall that sets can be infinite.

Set $A =$ the set of all odd integers

Set $B = $ the set of all even integers

What do they share in common?

Nothing. They share nothing in common.

What would their intersection be?

The intersection of two mutually exclusive sets is what is known as the Null Set or the Empty Set. This means a set with nothing inside of it. And yes, that IS a valid set.

What is the notation?

$$null \ set = empty \ set = \{\varnothing\}$$