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 \((P \cap Q)'\).
Verified Correct Answer: .
Step-by-Step Mathematical Solution
\(P = {..., -5, -4, -3, -2, -1}\)
\(Q = {..., -5, -3, -1, 1, 3, 5, ...}\)
\(R = {-2, -1, 0, 1, 2, 3, 4, 5, 6}\)
(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) \(Q = {..., -5, -3, -1, 1, 3, 5,...}\)
\(P \cap Q = {..., -7, -5, -3, -1}\)
\((P \cap Q)' = {..., -8, -6, -4, -2, 0, 1, 2, 3, ...}\)
Source: Myschool Past Questions Archive (Record #54566)