Question

If $A=\{xϵN:x<6\}$
$B=\{3,6,9\}$
$C=\{xϵN:2x-5\le 8\}$

then, find which of the following options are correct?

• A. $A\cap B=\left\{3\right\}$
• B. $A\cup B=\left\{3\right\}$
• C. $A\cup (B\cap C)=(A\cup B)\cap (A\cup C)$
• D. None of the above

Answer 1

Answer: (A), (C)

$A\cap B=\left\{3\right\}$
$A\cup (B\cap C)=(A\cup B)\cap (A\cup C)$

Given, $A=\{xϵN:x<6\}$ $=\{1,2,3,4,5\}$,
$B=\{3,6,9\}$
and $C=0$
$\Rightarrow 2x-5\le 8$
$\Rightarrow 2x\le 13$
$\Rightarrow x\le \frac{13}{2}=6\cdot 5$
$\Rightarrow x\le 6\cdot 5$
Therefore, $A\cap B=\left\{3\right\}$