Question

Let $P=\{x|x$ is a multiple of $3$ and less than $100$ ,$x$ $\in$ $N\}$
$Q=\{x|x$ is a multiple of $10$ and less than $100$, $x$ $\in$ $N\}$

• A. $Q\subset P$
• B. $P\cup Q=$ $\{x|x$ is multiple of 30$;$ $x\in N$$\}$
• C. $P\cap Q=\varphi$
• D. $P\cap Q=$ $\{x|x$ is a multiple of 30$;$ $x\in N$$\}$

Answer 1

The correct option is D $P\cap Q=$ $\{x|x$ is a multiple of 30$;$ $x\in N$$\}$

P = $\{3,6,9,12,15,18,21,24,27,30...,60,...,90,....,99\}$
Q = $\{10,20,30,40,50,60,70,80,90\}$
Then looking at the multiple choices we get
$P\cap Q$= $\{30,60,90\}$
$\Rightarrow$P $\cap$ Q = {x$\mid$ x is a multiple of 30 x$ϵ$ N}