Question

If $A=\{1,2,3\}$ and $B=\{3,8\}$, then $(A\cup B)\times (A\cap B)$ is equal to

• A. $\left\{\right(8,3),(8,2),(8,1),(8,8\left)\right\}$
• B. $\left\{\right(1,2),(2,2),(3,3),(8,8\left)\right\}$
• C. $\left\{\right(3,1),(3,2),(3,3),(3,8\left)\right\}$
• D. $\left\{\right(1,3),(2,3),(3,3),(8,3\left)\right\}$

Answer 1

The correct option is D $\left\{\right(1,3),(2,3),(3,3),(8,3\left)\right\}$

Given, $A=\{1,2,3\}$ and $B=\{3,8\}$,

Therefore, $A\cup B=\{1,2,3\}\cup \{3,8\}=\{1,2,3,8\}$
and $A\cap B=\{1,2,3\}\cap \{3,8\}=\left\{3\right\}$
$\therefore (A\cup B)\times (A\cap B)=\{1,2,3,8\}\times \left\{3\right\}$
$=\left\{\right(1,3),(2,3),(3,3),(8,3\left)\right\}$