Find Complements of Sets A, B and C
Let \[ U=\{1,2,3,4,5,6,7,8,9\} \] \[ A=\{1,2,3,4\} \] \[ B=\{2,4,6,8\} \] \[ C=\{3,4,5,6\} \] Find:
(i) \(A’\)
(ii) \(B’\)
(iii) \((A \cap C)’\)
(iv) \((A \cup B)’\)
(v) \((A’)’\)
(vi) \((B-C)’\)
Solution
(i) \[ A’=\{5,6,7,8,9\} \]
(ii) \[ B’=\{1,3,5,7,9\} \]
(iii) \[ A \cap C=\{3,4\} \]
\[ (A \cap C)’=\{1,2,5,6,7,8,9\} \]
(iv) \[ A \cup B=\{1,2,3,4,6,8\} \]
\[ (A \cup B)’=\{5,7,9\} \]
(v) \[ (A’)’=A=\{1,2,3,4\} \]
(vi) \[ B-C=\{2,8\} \]
\[ (B-C)’=\{1,3,4,5,6,7,9\} \]