Question

IfA = {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}