If $P=\{a, b, c\}$ and $Q=\{r\},$ form the sets $P \times Q$ and $P \times Q$ Are these two products equal?

Vedclass pdf generator app on play store
Vedclass iOS app on app store

By the definition of the cartesian product.

$P \times Q =\{(a, r),(b, r),(c, r)\}$ and $Q \times P =\{(r, a),(r, b),(r, c)\}$

Since, by the definition of equality of ordered pairs, the pair $(a, r)$ is not equal to the pair $(r, a),$ we conclude that $P \times Q \neq Q \times P$

However, the number of elements in each set will be the same.

Similar Questions

If $A = \{ 1,\,2,\,3,\,4\} $; $B = \{ a,\,b\} $ and $f$ is a mapping such that $f:A \to B$, then $A \times B$ is

Let $A=\{1,2\}, B=\{1,2,3,4\}, C=\{5,6\}$ and $D=\{5,6,7,8\} .$ Verify that

$A \times(B \cap C)=(A \times B) \cap(A \times C)$

If two sets $A$ and $B$ are having $99$ elements in common, then the number of elements common to each of the sets $A \times B$ and $B \times A$ are

If $\left(\frac{x}{3}+1, y-\frac{2}{3}\right)=\left(\frac{5}{3}, \frac{1}{3}\right),$ find the values of $x$ and $y$

If $A=\{-1,1\},$ find $A \times A \times A.$