Consider Statement 1: All prime numbers greater than 3 are equal to a multiple of six, plus 1 or minus 1.

Let P(x) be the statement x is a prime number.

Let Q(x) be the statement x is greater than 3.

Let R(x) be the statement x % 6 = 1 or x % 6 = 5. (i.e. x is a multiple of 6, plus or minus 1)

Let U be the domain of x. (% represents the modulo operation in this question.)

a.Given the following definitions of U, translate the above statement (Statement 1) into an expression of predicate logic. (using P(x), Q(x), R(x))

i. U = all prime numbers greater than 3.

ii. U = all prime numbers.

iii. U = all positive integers.