In this problem the following notation is used for the set of integers and three of its subsets:

The set of integers: Z

The set of silly integers: S

The set of proud integers: P

The set of wild integers: W

(It is not necessary to know what is meant by a silly, proud or wild integer to do this problem.) Using only the symbols 8, Z, S, P, W, , , , , , , =, {, }, ),(, and (not equal symbol),

express the following statements.

(a) 8 is a silly or wild integer.

(b) All wild integers are silly.

(c) Every proud integer is wild but not silly.

(d) There are integers that are not silly and not wild.