Question

If A = $A=\{x\in W:5<x<10\},B=\{3,4,5,6,7\}andC=\{x=2n;n\in Nandn\le 4\}$. Find :

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

(ii) $(B\cup A)\cap (B\cup C)$
(iii) $B\cup (A\cap C)$
(iv) $(A\cap B)\cup (A\cap C)$

Name the sets which are equal

Answer 1

A = B = x = 2n When n = 1, x = $2\times 1$ = 2 When n = 2, x = $2\times 2$ = 4 When n = 3, x = $2\times 3$ = 6 When n = 4, x = $2\times 4$ = 8 $\therefore$ C = $\{2,4,6,8\}$ (i)$B\cup C=\{3,4,5,6,7\}\cup \{2,4,6,8\}=\{3,4,5,6,7\}A\cap (B\cup C)=\{6,7,8\}$Ans. (ii)$B\cup A=\{3,4,5,6,7\}\cup \{6,7,8,9\}\{3,4,5,6,7,8,9\}(B\cup A)\cap (B\cup C)=\{3,4,5,6,7,8,9\}\cap \{2,3,4,5,6,7,8\}=\{3,4,5,6,7,8\}$Ans. (iii)$(A\cap C)=\{6,7,8,9\}\cap \{2,4,6,8\}=\{6,8\}B\cup (A\cap C)=\{3,4,5,6,7\}\cup \{6,8\}=\{3,4,5,6,7,8\}$Ans. (iv) $(A\cap B)=\{6,7,8,9\}\cap \{3,4,5,6,7\}=\{6,7\}\therefore (A\cap B)\cup (A\cup C)=\{6,7\}\cup \{6,8\}=\{6,7,8\}$ Ans.