Question

Given $M=\{5,6,7\}$ and $N=\{6,8,10\}$ find element of $(M\cup N)\times N$

• A. $\{5,6\}$
• B. $\{5,8\}$
• C. $\{5,10\}$
• D. All of the above

Answer 1

The correct option is D All of the above

For two non-empty sets $A$ and $B$, the Cartesian product $A\times B$ is the set of all ordered pair of elements from $A$ and $B$.
$A\times B=\left\{\right(x,y):x\in A,y\in B\}$
If $A=\{a,b\}$ and $B=\{x,y\},$
then $A\times B=\left\{\right(a,x);(a,y);(b,x);(b,y\left)\right\}$

here, $A=M\cup N$ and $B=N$

$A=M\cup N$ ={ $5,6,7,8,10$ }

$B=${$6,8,10$}

$A\times B=(M\cup N)\times N=(A,6),(A,8),(A,10)$

hence A,B,C all are correct so answer is D