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Check whether the following pair of statements is negation of

Question

Check whether the following pair of statements is negation of each other. Give reasons for the answer
(i) $x + y = y + x$ is true for every real numbers $x$ and $y$
(ii) There exists real number $x$ and $y$ for which $x + y = y + x$

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Check whether the following pair of statements is negation of each other. Give reasons for the answer
(i)

x + y = y + x

is true for every real numbers

x

and

y

(ii) There exists real number

x

and

y

for which

x + y = y + x

11 mins ago

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Text solutionVerified

The negation of statement (i) is as follows
There exists real number

x

and

y

for which

x + y

\neq =

y + x

. This is not the same as statement (ii).
Thus the given statements are not the negation of each other

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Question Text	Check whether the following pair of statements is negation of each other. Give reasons for the answer (i) $x + y = y + x$ is true for every real numbers $x$ and $y$ (ii) There exists real number $x$ and $y$ for which $x + y = y + x$
Answer Type	Text solution:1
Upvotes	150