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

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

Answer 1

$A=\{3,5,7,9,11\},B=\{7,9,11,13\},C=\{11,13,15\}$ and $D=\{15,17\}$
(i) $A\cap B=\{7,9,11\}$
(ii) $B\cap C=\{11,13\}$
(iii) $A\cap C\cap D=(A\cap C)\cap D=\left\{11\right\}\cap \{15,17\}=\varphi$
(iv) $A\cap C=\left\{11\right\}$
(v) $B\cap D=\varphi$
(vi) $A\cap (B\cup C)=(A\cap B)\cup (A\cap C)$
$=\{7,9,11\}\cup \left\{11\right\}=\{7,9,11\}$
(vii) $A\cap D=\varphi$
(viii) $A\cap (B\cup D)=(A\cap B)\cup (A\cap D)$
$=\{7,9,11\}\cup \varphi =\{7,9,11\}$
(ix) $(A\cap B)\cap (B\cup C)=\{7,9,11\}\cap \{7,9,11,13,15\}=\{7,9,11\}$
(x) $(A\cup D)\cap (B\cup C)=\{3,5,7,9,11,15,17\}\cap \{7,9,11,13,15\}$
$=\{7,9,11,15\}$