Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9},

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) $(B-C)^{\prime}=\{1,3,4,5,6,7,9\}$

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