Question

State True or False for the following statement:
If$P=\{1,2\},$ then
$P\times P\times P={\{}_{(1,2,2),(2,1,1)}^{(1,1,1),(2,2,2),}\}$

Answer 1

Apply relevant property of Cartesian product

Given: $P=\{1,2\}$

$\Rightarrow n\left(P\right)=2$

$n(P\times P\times P)=n\left(P\right)\times n\left(P\right)\times n\left(P\right)$

$=2\times 2\times 2$

$=8$elements

But given $P\times P\times P={\{}_{(1,2,2),(2,1,1)}^{(1,1,1),(2,2,2),}\}$

i.e.,n$(P\times P\times P)=4$ element

Hence, given statement is false