Assertion : $x + y = y + x$ is true for every real number $x$ and $y$ . Negation of this statement is There exists real numbers $x$ and $y$ for which $x + y = y + x$ . Reason: These statements are not negation of each other as they can be true at the same time.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Given assertion is correct
The negation of statement $x + y = y + x$ is again $x + y = y + x$
The statements are not negation of each other as they can be true at the same time
Therefore the assertion is correct and the reason is correct explanation of assertion
Therfore option $A$ is correct

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Similar questions

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Which of the following is correct?

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Assertion: All the points (1, 0), (-1, 0), (2, 0) and (5, 0) lie on the x – axis.
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Choose the correct option.

Q. Assertion: x = 3 is a line parallel to the y-axis.
Reason: Any line parallel to the y-axis is y = k, where k ∈ R.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

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Assertion :x+y=y+x is true for every real number x and y. Negation of this statement is There exists real numbers x and y for which x+y=y+x. Reason: These statements are not negation of each other as they can be true at the same time.

Assertion : $x + y = y + x$ is true for every real number $x$ and $y$ . Negation of this statement is There exists real numbers $x$ and $y$ for which $x + y = y + x$ . Reason: These statements are not negation of each other as they can be true at the same time.