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NCERT Class XI Mathematics - Mathematical Reasoning - Solutions
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Question : 8 of 25
Marks:
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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.
(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.
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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