Question

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 into an expression of predicate logic.

i. U = all prime numbers greater than 3.

ii. U = all prime numbers.

iii. U = all positive integers.

Answer 1

Explanation: P(x): Prime number; Q(x): Prime number greater than 3; R(x): Positive integer and U(x): All prime numbers

i) {∀x) (Q(x) ⇒ (U(x)}

ii) {∀x) (P(x) ⇒ (U(x)}

iii) {∀x) (R(x) ⇒(U(x)}