Question

If $P=\{x:x<3,x\in N\},Q=\{x:x\le 2,x\in W\},$ then $(P\cup Q)\times (P\cap Q)$ is

• A. $\left\{\right(0,1),(0,2),(1,1),(1,2),(2,1),(2,2\left)\right\}$
• B. $\left\{\right(0,1),(0,2),(0,3),(1,1),(1,2),(1,3),(2,1),(2,2),(2,3)\}$
• C. $\varphi$
• D. $\left\{\right(0,1),(0,2),(0,3\left)\right\}$

Answer 1

The correct option is A $\left\{\right(0,1),(0,2),(1,1),(1,2),(2,1),(2,2\left)\right\}$

$P=\{1,2\},Q=\{0,1,2\}P\cap Q=\{1,2\},P\cup Q=\{0,1,2\}$
$\therefore (P\cup Q)\times (P\cap Q)=\left\{\right(0,1),(0,2),(1,1),(1,2),(2,1),(2,2\left)\right\}$