Q35 of 44 Page 1

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that
(i) (A ∪ B)’ = A’ ∩ B’
(ii) (A ∩ B)’ = A’ ∪ B’


(i) A ∪ B = {2, 3, 4, 5, 6, 7, 8}
(A ∪ B)’ = {1, 9}
A’ ∩ B’ = {1, 3, 5, 7, 9} ∩ {1, 4, 6, 8, 9} = {1, 9}
Therefore (A ∪ B)’ = A’ ∩ B’
(ii) A ∩ B = {2}
(A ∩ B)’ = {1, 3, 4, 5, 6, 7, 8, 9}
A’ ∪ B’ = {1, 3, 5, 7, 9} ∪ {1, 4, 6, 8, 9} = {1, 3, 4, 5, 6, 7, 8, 9}
Therefore (A ∩ B)’ = A’ ∪ B’

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33
If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:
(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g}
(iv) D = {f, g, h, a}

34
Taking the set of natural numbers as the universal set, write down the complements of the following sets
(i) {x : x ∈ N and x is even}
(ii) {x : x ∈ N and x is odd}
(iii) {x : x ∈ N and x = 3n for some n ∈ N}
(iv) {x : x is a prime number}
(v) {x : x ∈ N and x is a perfect square}
(vi) {x : x ∈ N and x is a perfect cube}
(vii) {x : x ∈ N and x + 5 = 8}
(viii) {x : x ∈ N and 2x + 5 = 9}
(ix) {x : x ∈N and x ≥ 7}
(x) {x : x ∈ N and x is a divisible by 3 and 5}

36
Draw appropriate Venn diagram for each of the following:
(i) (AB)’, (ii) A’ B’, (iii) (AB)’, (iv) A’ B’

37
If X and Y are two sets such that n(X) = 17, n(Y) = 23, n(X ∪ Y) = 38, find n(X ∩ Y).