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}))
= ({2, 4, 6, 8} cap { })
= ({ })
(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})