4
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.
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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Solution
The
negation of statement (i) is as follows.
There
exists real number x
and y
for which x
+ y
≠
y +
x.
This is not the same as statement (ii).
Thus,
the given statements are not the negation of each other.
The negation of statement (i) is as follows.
There exists real number x and y for which x + y ≠ 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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