The function is , where and are integers with no common factors.

(a)

Consider the value of (even).

Consider the value of (odd).

Substitute the values of and in .

.

For the condition , take .

= Undefined.

Thus, the statement is true.

(b)

Consider the value of (even).

Consider the value of (odd).

Substitute the values of and in .

.

For the condition , take .

= Defined.

Thus, the statement is false.

(c)

Consider the value of .

Substitute the value of in .

for all values of .

Thus, the statement is true.

(a) True.

(b) False.

(c) True.