Theory question 101
SetsGiven that μ = {x: 1 < x < 20, where x is an integer}, P = {x: x is a multiple of 3} and Q = {x: x is a prime number} where P and Q are subsets of μ, find: (a) P ∩ Q′; (b) P′ ∪ Q; (c) (P ∪ Q)′.
Show the model answer
Model answer
μ = {2, 3, …, 19}; P = {3, 6, 9, 12, 15, 18}; Q = {2, 3, 5, 7, 11, 13, 17, 19}
(a) P ∩ Q′ = {6, 9, 12, 15, 18} (3 is prime, so it is not in Q′)
(b) P′ = {2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19}; P′ ∪ Q = {2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19}
(c) P ∪ Q = {2, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19}; (P ∪ Q)′ = {4, 8, 10, 14, 16}
Explanation
List μ, P and Q first; remember 3 is both a multiple of 3 and prime.