The universal set (varepsilon) is the set of all integers and the subset P, Q, R of (varepsilon) are given by:
(P = {x : x < 0} ; Q = {… , -5, -3, -1, 1, 3, 5} ; R = {x : -2 leq x < 7})
(a) Find (Q cap R).
(b) Find (R’) where R’ is the complement of R with respect to (varepsilon).
(c) Find (P’ cup R’)
(d) List the members of ((P cap Q)’).
Explanation
(P = {…, -5, -4, -3, -2, -1})
(Q = {…, -5, -3, -1, 1, 3, 5, …})
(R = {-2, -1, 0, 1, 2, 3, 4, 5, 6})
(a) (Q cap R = {-1, 1, 3, 5})
(b) (R’ = {…, -5, -4, -3, 7, 8, …})
(c) (P’ = {0, 1, 2, 3, …})
(P’ cup R’ = {-5, -4, -3, 0, 1, 2, 3, …})
(d) (Q = {…, -5, -3, -1, 1, 3, 5,…})
(P cap Q = {…, -7, -5, -3, -1})
((P cap Q)’ = {…, -8, -6, -4, -2, 0, 1, 2, 3, …})