Question:
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find
(i) $A^{\prime}$
(ii) $B^{\prime}$
(iii) $(A \cap C)^{\prime}$
(iv) $(A \cup B)^{\prime}$
(v) $\left(A^{\prime}\right)^{\prime}$
(vi) $(B-C)^{\prime}$
Solution:
Given:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B= {2, 4, 6, 8} and C = {3, 4, 5, 6}
(i) $A^{\prime}=\{5,6,7,8,9\}$
(ii) $B^{\prime}=\{1,3,5,7,9\}$
(iii) $(A \cap C)^{\prime}=\{1,2,5,6,7,8,9\}$
(iv) $(A \cup B)^{\prime}=\{5,7,9\}$
(v) $\left(A^{\prime}\right)^{\prime}=\{1,2,3,4\}=A$
(vi) $(B-C)^{\prime}=\{1,3,4,5,6,7,9\}$