if U = {a, b, c} and A = {a, c, d, e} then verify that:

(i) (A ∪ B)’ = (A’ ∩ B’)

(ii) (A ∩ B)’ = (A’ ∪ B’)

Which of the following sets are pairs of disjoint sets? Justify your answer.

(i) A = {3, 4, 5, 6} and B = {2, 5, 7, 9}

(ii) C = {1, 2, 3, 4, 5} and D = {6, 7, 9, 11}

(iii) E = {x : x ϵ N, x is even and x < 8}

F = {x : x = 3n, n ϵ N, and x < 4}

(vi) G = {x : x ϵ N, x is even} and H {x : x ϵ N, x is prime}

(v) J = {x : x ϵ N, x is even} and K = {x : x ϵ N, x is odd}

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A A = {1, 2, 3, 4,}, B = {2, 4, 6, 8} and = {1, 4, 5, 6}, find:

(i) A’

(ii) B’

(iii) C’

(iv) (B’)’

(v) (A ∪ B)’

(vi) (A ∩ C)’

(vii) ( B – C)’

if U is the universal set and A U then fill in the blanks.

(i) A ∪ A’ = ….

(ii) A ∩ A’ = ….

(iii) ϕ ‘∩ A = ….

(iv) U’ ∩ A = ….

If A = {a, b, c, d, e}, B = {a, c, e, g}, verify that:

(i) A ∪ B = B ∪A

(ii) A ∪ C = C ∪ A

(iii) B ∪ C = C ∪ B

(iv) A ∩ B = B ∩ A

(v) B ∩ C = C ∩ B

(vi) A ∩ C = C ∩ A

(vii) (A ∪ B ∪ C = A ∪ (B ∪ C)

(viii) (A ∩ B) ∩ C = A ∩ (B ∩ C)