Question

$A=\left\{1,2,3\right\}\text{and}B=\left\{3,8\right\}$; then $(A\cup B)\times (A\cap B)$ is

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

Answer 1

The correct option is B

$\left\{(1,3),(2,3),(3,3),(8,3)\right\}$

Explanation for correct answer:

Applying required operation on sets:

$A=\left\{1,2,3\right\}\text{and}B=\left\{3,8\right\}$

From the given question:

$A\cup B=\left\{1,2,3,8\right\}$

and $A\cap B=\left\{3\right\}$

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

Hence, we can conclude that Option(B) is correct.