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3. Check whether the following pair of statements are negation of each other. Give reasons for your answer.
(i) is true for every real numbers
and
.
(ii) There exists real numbers and
for which
.
Answers (1)
p: is true for every real numbers
and
.
q: There exists real numbers and
for which
.
The negation of p is:
There exists no real numbers x and y for which
which is not equal to q.
Hence the given pair of statements are not negation of each other.
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