Hello Mel

Here is the problem.

Suppose and are nonempty sets and is a function. Let and be subsets of . Prove that

We do this by showing that and

So, for the first part:

Suppose . Then for some , , and .

or [Note: throughout this proof 'or' means 'inclusive or'. So or means oror both.

or

or

So

(1)

For the second part:

Suppose

Then or

Then for some , and or

So

(2)

So, from (1) and (2):

Grandad