Let Q : N {true,false} be a predicate with domain the natural numbers N = {0, 1, 2, . . .} and defined by the statement Q(k) = "k is a prime number". Identify the following propositions as true or false. Unless otherwise stated, only use

results from lectures,

the fact that the only even prime is 2, and

basic arithmetic with natural numbers.

Show all you working and reasoning.

(a) Q(1), Q(2), Q(3), Q(4)

(b) For all k N, k>2, we have Q(k)Q(k+3).

(c) k N : Q(2k)