Question

State whether each of the following statements is true or false. If the statement is false, rewrite the given statement correctly:

If $\mathrm{P}=\{\mathrm{m},\mathrm{n}\}$ and $\mathrm{Q}=\{\mathrm{n},\mathrm{m}\}$ then $\mathrm{P}\times \mathrm{Q}=\left\{\right(\mathrm{m},\mathrm{n}),(\mathrm{n},\mathrm{m}\left)\right\}$

Answer 1

Explanation:

If $P=\{m,n\}\mathrm{and}Q=\{n,m\}$. Then,

$P\times Q=\left\{\right(m,n),(m,m),(n,n),(n,m\left)\right\}$

The given value of $P\times Q$ is incorrect.

Hence, the given statement is false.

The correct statement is,

If $P=\{m,n\}$ and $Q=\{n,m\}$ then $P\times Q=\left\{\right(m,n),(m,m),(n,n),(n,m\left)\right\}$.