Show that if A and B are sets, then

Solution :

Step 1:

In this problem we have to show these conditions , where A and B are two sets.

Formulas: 1. = X - B,

2. A A = A

3. AA =

Definitions:

Union: the union of the sets A and B , denoted by , which is the set that contains those element that are either in A or in B , or in both.

Therefore = { }.

Intersection : the intersection of the sets A and B , it is denoted by , which is the set containing those elements in both A and B.

Therefore .

Set difference : the difference of A and B is denoted by A -B, which is the set containing the element of A that are not in B .

A - B = { }=