A = {2, 4, 6, 8}, B = {2, 3, 7, 9} and C = {x : 3 < x < 9} are subsets of the universal set U = {2, 3, 4, 5, 6, 7, 8, 9}. Find
(a) \(A \cap (B’ \cap C’)\) ;
(b) \((A \cup B) \cap (B \cup C)\).
Explanation
\(U = {2, 3, 4, 5, 6, 7, 8, 9}\)
\(A = {2, 4, 6, 8}\)
\(B = {2, 3, 7, 9}\)
\(C = {4, 5, 6, 7, 8}\)
(a) \(A \cap (B' \cap C')\) = \({2, 4, 6, 8} \cap ({4, 5, 6, 8} \cap {2, 3, 9})\)
B' = 4,5,6,8
C' = 2,3
B' n C' = Ø
\(A \cap (B' \cap C')\) = \({2, 4, 6, 8} \cap { }\) Ø
= Ø
(b) \((A \cup B) \cap (B \cup C)
= {2, 3, 4, 6, 7, 8, 9} \cap {2, 3, 4, 5, 6, 7, 8, 9}\)
= \({2, 3, 4, 6, 7, 8, 9}\)