Question

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

• A. $\left\{\right(1,3),(2,3),(3,1),(3,2),(1,1),(2,1),(1,2\left)\right\}$
• B. $\left\{\right(1,3),(3,1),(3,2),(2,3\left)\right\}$
• C. $\left\{\right(1,3),(2,3),(3,1),(3,2),(1,1\left)\right\}$
• D. None of these

Answer 1

The correct option is A

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

Find the value of $\mathbf{(}\mathit{A}\mathbf{}\mathbf{\times }\mathbf{}\mathit{B}\mathbf{)}\mathbf{\cup }\mathbf{(}\mathit{B}\mathbf{}\mathbf{\times }\mathbf{}\mathit{A}\mathbf{)}$:

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

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

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

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

Hence, the correct option is A.