Question

If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1,4, 7,10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12}. Write down the sets.

(i) A ∪ B

(ii) B ∩ C

(iii) A – B

(iv) B ∩ C’

(v) A ∪ B ∪ C

(vi) A ∩ (B ∪ C)

Answer 1

U = {x/x ∈ N, 1 ≤ x ≤ 12} = {1, 2, 3, …., 12} A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12}

(i) A ∪ B = {1, 2, 4, 6, 7, 10, 11}

(ii) B ∩ C = { }

(iii) A – B = {1, 10}

(iv) C’ = {1, 2, 4, 6, 7, 10, 11}

∴ B ∩ C’ = {2, 4, 6, 7, 11}

(v) A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

(vi) B ∪ C = {2, 3, 4, 5, 6, 7, 8, 9, 11, 12}

∴ A ∩ (B ∪ C) = {4, 7}