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NCERT Class XI Mathematics - Mathematical Reasoning - Solutions
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Question : 4 of 25
Marks:
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Are the following pairs of statements negations of each other: (i) The number x is not a rational number. The number x is not an irrational number. (ii) The number x is a rational number. The number x is an irrational number.
Solution:
(i) Let p : The number x is not a rational number. q : The number x is not an irrational number. Now, ~p : The number x is a rational number. ~q : The number x is an irrational number. ∴ ~p = q and ~q = p Thus, p and q are negations of each other. (ii) Let p : The number x is a rational number. q : The number x is an irrational number. Now, ~p: The number x is not a rational number. ~q: The number x is not an irrational number. ∴ ~p = q and ~q = p Thus, p and q are negations of each other.
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