Question

If $P=\{a,b,c\}$ and $Q=\{r\}$, then

• A. $P\times Q=Q\times P$
• B. $P\times Q\ne Q\times P$
• C. $P\times Q\subset Q\times P$
• D. None of these

Answer 1

Answer: (B)

Given $P=\{a,b,c\}$ and $Q=\{r\}$
$P\times Q=\{(a,r),(b,r),(c,r)\}$
$Q\times P=\{(r,a),(r,b),(r,c)\}$
Since, by the definition of equality of ordered pairs,
the pair $(a,r)$ is not equal to the pair $(r,a)$,
we conclude that $P\times Q\ne Q\times P$
However, the number of elements in each set will be the same.