Given A={x ∈ Z : x is even}, B={x ∈ Z : x is prime number}, C={x ∈ Z : x is odd}, and D={5, 7, 8, 12, 13, 15}.

(a) Find D - (A ∪ B)

(b) Find D - (A ∪ C)

(c) Find D - (A ∩ B)

(d) Are A and B Disjoint? Explain.

(e) Are A and C Disjoint? Explain

a) {15}

b) { }

c) D or {5, 7, 8, 12, 13, 15}

d) no

e) yes

Step-by-step explanation:

a) AUB: even or prime

D - (AUB) = {15}

b) AUC: even or odd; basically all integers

D - (AUC) = { }

c) A∩B : even and prime, that's only 2

D - (A∩B) = {5, 7, 8, 12, 13, 15} = D

d) A and B, both contain 2

Not disjoint

e) A and C are disjoint because no number can be both, even and odd