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}

State whether each of the following statements is true or false. Justify your answer.
(i) {2, 3, 4, 5} and {3, 6} are disjoint sets
(ii) {a, e, i, o, u} and {a, b, c, d} are disjoint sets
(iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoints sets
(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.

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)’

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}

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’