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

2/9 and 4/9

Step-by-step explanation:

There are 3 * 3 = 9 possible outcomes of spinning the spinners. Out of those, there are only 2 ways to achieve a product of 6 (2 and 3 or 6 and 1) so the answer to B is 2/9. For C, there are 4 ways for the total to be greater than 10 (12, 18, 20, 30) so the answer is 4/9.