Show that if A,b, and C are sets, then

a) by showing each side is a subset of the other side.

b) using a membership table.

Step 1:

In this problem we have to show that by each side is a subset of the other side.

Step 2: some 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 .

Complement: let U is the universal set and A be any set then the complement of A , denoted by , that it is a set of elements not in A.

i.e.