The domain of discourse is the set of positive integers. Let (x, y, z) = z is the product of x and y. Define each of the following in terms of . You may also use = in your formula to compare integers for equality.

(A) Write a formula that means there exists an x that is the multiplicative identity. Recall that a multiplicative identity is a number that leaves unchanged any number by which it is multiplied.

(B) Let n be some (fixed) positive integer. Write a formula that means n is a prime number. Note that n should not be quantified in your formula because it is already a fixed value.(Added challenge: use your multiplicative identity formula).

(C) Write a formula that symbolizes the commutative property for the multiplication of integers (i.e. x y = y x).

(D) Write a formula that symbolizes the associative law for the multiplication of integers (i.e. x (y z) = (x y) z).