EXAMPLE 1.2.1

Let U = {a, b, c, d, e, f}

A = {a, c, e, f}

B = {c, d, e}

C = {e, f}

SOLUTIONS

1. "A complement" is the set of elements that are in U but aren't in A.

2.

3.

4. "B union C" is formed by combining the elements of the two sets into one larger set:

5. "A intersect C" is the set of elements that those two sets have in common:

6.

7. is the set of elements that are in U but aren't in .

First, we find that .

Thus,

8. To find we need to first find "A complement" and "B complement," and then perform the union of those two sets.

So,

9. To find we must first find and then perform the intersection of that set with C.

, C = {e,f}, so

10. To find we must first find and then perform the union of that set with A. Now, A = {a,c,e,f} and (from #9 above) , so