A = {2, 4, 6, 8}, B = {2, 3, 7, 9} and C = {x…

Question 1 Report

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) \((A \cup B) \cap (B \cup C)\).

Answer

Answer Details

The universal set is \(U = \{2,3,4,5,6,7,8,9\}\), with \(A = \{2,4,6,8\}\), \(B = \{2,3,7,9\}\) and \(C = \{x : 3 < x < 9\} = \{4,5,6,7,8\}\).

Complements within \(U\):

(a) \(B' \cap C' = \{4,5,6,8\} \cap \{2,3,9\} = \varnothing\).

Therefore \(A \cap (B' \cap C') = A \cap \varnothing = \varnothing\) (the empty set).

(b) First form the unions:

\[(A \cup B) \cap (B \cup C) = \{2,3,4,6,7,8,9\}.\]

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) \(A \cap (B' \cap C')\) ;...