Question 1:
Let 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}.
Find
(i) A΄
(ii) B΄
(iii) (A ∪ C)΄
(iv) (A ∪ B)΄
(v) (A΄)΄
(vi)(B−C)΄
Answer
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}
(i) A΄={5, 6, 7, 8, 9}
(ii) B΄ = {1, 3, 5, 7, 9}
(iii) A ∪ C={1, 2, 3, 5, 6, 8}
∴ (A ∪ C)΄ = {7, 8, 9}
(iv) A ∪ B = {1, 2, 3, 4, 6, 8}
(A ∪ 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}
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