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}

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(ii) $B ∩C$ = {11, 13}

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(iii) $A ∩C ∩D =${ $A ∩C$} $∩D$ = {11} $\cap${15, 17} = $\phi$

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(iv) $A ∩C =$ {11}

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(v) $B ∩D = \phi$

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(vi) $A ∩(B ∪ C) = (A ∩B) (A ∩C)$
= {7, 9, 11} {11} = {7, 9, 11}

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(vii) $A\cap D = \phi$

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(viii) $A ∩(B ∪ D) = (A ∩B) (A ∩D)$
= {7, 9, 11} Φ= {7, 9, 11}

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

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