Question

If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and

D = {15, 17}; find

(i) A ∩ B

(ii) B ∩ C

(iii) A ∩ C ∩ D

(iv) A ∩ C

(v) B ∩ D

(vi) A ∩ (B∪C)

(vii) A ∩ D

(viii)A ∩ (B∪D)

(ix) (A ∩ B) ∩ (B∪C)

(x) (A∪D) ∩ (B∪C)

Answer 1

(i) A ∩ B = {7, 9, 11}

(ii) B ∩ C = {11, 13}

(iii) A ∩ C ∩ D = { A ∩ C} ∩ D = {11} ∩ {15, 17} = Φ

(iv) A ∩ C = {11}

(v) B ∩ D = Φ

(vi) A ∩ (B∪ C) = (A ∩ B)∪ (A ∩ C)

= {7, 9, 11}∪ {11} = {7, 9, 11}

(vii) A ∩ D = Φ

(viii) A ∩ (B∪ D) = (A ∩ B) (A ∩ D)

= {7, 9, 11} ∪Φ = {7, 9, 11}

(ix) (A ∩ B) ∩ (B∪ C) = {7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11}

(x) (A∪ D) ∩ (B ∪C) = {3, 5, 7, 9, 11, 15, 17) ∩ {7, 9, 11, 13, 15}

= {7, 9, 11, 15}