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Q. 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)'
Answers (1)
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′ = U - A = {5,6,7,8,9}
(ii) B′ = U - B = {1,3,5,7,9}
(iii) A C = {1,2,3,4,5,6}
(A C)′ = U - (A
C) = {7,8,9}
(iv) (A B) = {1,2,3,4,6,8}
(A B)′ = U - (A
B) = {5,7,9}
(v) (A')' = A = { 1, 2, 3, 4}
(vi) (B – C) = {2,8}
(B – C)' = U - (B – C) = {1,3,4,5,6,7,9}
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