Question

If $A=\{1,2,3,4,5\},B=\{4,5,6,7,8\},C=\{7,8,9,10,11\}andD=\{10,11,12,13,14\}.$. Find:

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

Answer 1

Given, $A=\{1,2,3,4,5\},B=\{4,5,6,7,8\}$

$C=\{7,8,9,10,11\}andD=\{10,11,12,13,14\}$

$A\cup D=\{1,2,3,4,5\}\cup \{10,11,12,13,14\}$

$A\cup D=\{1,2,3,4,5,10,11,12,13,14\}...\left(1\right)$

$\mathrm{Sin}ceB=\{4,5,6,7,8\}andC=\{7,8,9,10,11\}$

$Now,(B\cup C)=\{4,5,6,7,8\}\cup \{7,8,9,10,11\}$

$(B\cup C)=\{45,6,7,8,9,10,11\}...\left(2\right)$

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

From (1) & (2), we have

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

$=\{1,2,3,4,5,10,11,12,13,14\}\cap \{4,5,6,7,8,9,10,11$

$(A\cup D)\cap (B\cup C)=\{4,5,10,11\}$

$Hence,(A\cup B)\cap (B\cup C)=\{4,5,10,11\}$