If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, ...

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NCERT Class XI Mathematics - Sets - Solutions

Question : 36 of 73

Marks: +1, -0

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)

Solution:

Here A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}

(i) A ∩ B = {3, 5, 7, 9, 11} ∩ {7, 9, 11, 13} = {7, 9, 11}

(ii) B ∩ C = {7, 9, 11, 13} ∩ {11, 13, 15} = {11, 13}

(iii) A ∩ C ∩ D = {3, 5, 7, 9, 11} ∩ {11, 13, 15} ∩ {15, 17} = ϕ

(iv) A ∩ C = {3, 5, 7, 9, 11} ∩ {11, 13, 15} = {11}

(v) B ∩ D = {7, 9, 11, 13} ∩ {15, 17} = ϕ

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

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

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

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