Question

If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find :

(i) $A\cap B$ (ii) $B\cap C$

(iii) $A\cap C\cap D$ (iv) $A\cap C$

(v) $B\cap D$ (vi) $A\cap (B\cup C)$

(vii) $A\cap D$ (viii) $A\cap (B\cup D)$

(ix) $(A\cap B)\cap (B\cup C)$

(x) $(A\cup D)\cap (B\cup C)$

Answer 1

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

(i) $A\cap B$ = {3, 5, 7, 9, 11} $\cap$ {7, 9, 11, 13}

= {7, 9, 11}

(ii) $B\cap C$ = {7, 9, 11, 13} $\cap$ {11, 13, 15}

= {11, 13}

(iii) $A\cap C\cap D$ = {3, 5, 7, 9, 11} $\cap$ {11, 13, 15} $\cap$ {15, 17} = $\Phi$

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

= {11}

(v) $B\cap D$ = {7, 9, 11, 13} $\cap$ {15, 17} = $\Phi$

(vi) $A\cap (B\cup C)$ = {3, 5, 7, 9, 11} $\cap$ ({7, 9, 11, 13} $\cup$ {11, 13, 15})

= {3, 5, 7, 9, 11} $\cap$ {7, 9, 11, 13, 15}

= {7, 9, 11}

(vii) $A\cap D$ = {3, 5, 7, 9, 11} $\cap$ {15, 17} = $\Phi$

(viii) $A\cap (B\cup D)$ = {3, 5, 7, 9, 11} $\cap$ ({7, 9, 11, 13} $\cup$ {15, 17})

= {3, 5, 7, 9, 11} $\cap$ {7, 9, 11, 13, 15, 17}

= {7, 9, 11}

(ix) $(A\cap B)\cap (B\cup C)$ = ({3, 5, 7, 9, 11} $\cap$ {7, 9, 11, 13}) $\cap$ ({7, 9, 11, 13} $\cup$ {11, 13, 15})

= {7, 9, 11} $\cap$ {7, 9, 11, 13, 15}

= {7, 9, 11}

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

= {3, 5, 7, 9, 11, 15, 17} $\cap$ {7, 9, 11, 13, 15}

= {7, 9, 11, 15}