Theory question 102
SetsThe Universal set is the set of all integers and the subjects P, Q, R of ε are given by
P = {x: x < 0}
Q = {…, −5, −3, −1, 1, 3, 5, …..}
R = {x: −2 ≤ x < 7}
(a) Find Q∩R. (b) Find R' where R' is the complement of R with respect to ε. (c) Find P'∩R'. (d) List the members of (P∩Q)'.
Show the model answer
Model answer
R = {−2, −1, 0, 1, 2, 3, 4, 5, 6}; Q is the set of odd integers
(a) Q∩R = {−1, 1, 3, 5}
(b) R' = {x: x < −2 or x ≥ 7} = {…, −5, −4, −3, 7, 8, 9, …}
(c) P' = {0, 1, 2, 3, …}, so P'∩R' = {7, 8, 9, …}
(d) P∩Q = {…, −5, −3, −1} (negative odd integers)
(P∩Q)' = {…, −6, −4, −2, 0, 1, 2, 3, 4, …}: all even integers together with the non-negative odd integers
Explanation
Since ε is all integers, a complement contains every integer not in the set.