Check whether the following pair of ...

NCERT Class XI Mathematics - Mathematical Reasoning - Solutions

Question : 8 of 25

Marks: +1, -0

Check whether the following pair of statements are negation of each other. Give reasons for your answer.

(i) x + y = y + x is true for every real numbers x and y.

(ii) There exists real numbers x and y for which x + y = y + x.

Solution:

Let p: x + y = y + x is true for every real numbers x and y.

q: There exists real numbers x and y for which x + y = y + x.

Now, ~p: There exists real numbers x and y for which x + y ≠ y + x.

Thus, ~p ≠ q.

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