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

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2.Relations and Functions

easy

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

Option A

Option B

Option C

Option D

Solution

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.

Standard 11

Mathematics

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

Solution

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