Question:
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A A = {1, 2, 3, 4,}, B = {2, 4, 6, 8} and = {1, 4, 5, 6}, find:
(i) $\mathbf{A}^{\text {' }}$
(ii) B'
(iii) $\mathbf{C}^{\text {' }}$
(iv) $\left(B^{\prime}\right)^{\prime}$
(v) $(\mathrm{A} \cup \mathrm{B})^{\prime}$
(vi) $(\mathbf{A} \cap \mathbf{C})^{\prime}$
(vii) $(\mathrm{B}-\mathrm{C})^{\prime}$
Solution:
Given; U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4,}, B = {2, 4, 6, 8} and C = {1, 4, 5, 6}
(i) $A^{\prime}=\{5,6,7,8,9\}$
(ii) $B^{\prime}=\{1,3,5,7,9\}$
(iii) $C^{\prime}=\{2,3,7,8,9\}$
(iv) $\left(B^{\prime}\right)^{\prime}=\{2,4,6,8\}$
(v) $(A \cup B)^{\prime}=\{5,7,9\}$
(vi) $(A \cap C)^{\prime}=\{2,3,5,6,7,8,9\}$
(vi) $(B-C)^{\prime}=\{1,3,4,5,6,7,9\}$