NCERT Class XI Mathematics - Mathematical Reasoning - Solutions
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Question : 19
Total: 25
Write the negation of the following statements:
(i) p: For every positive real number x, the number x – 1 is also positive.
(ii) q: All cats scratch.
(iii) r: For every real number x, either x > 1 or x < 1
(iv) s: There exists a number x such that 0 < x < 1.
(i) p: For every positive real number x, the number x – 1 is also positive.
(ii) q: All cats scratch.
(iii) r: For every real number x, either x > 1 or x < 1
(iv) s: There exists a number x such that 0 < x < 1.
Solution:
(i) ~p: There exists a positive real number x such that x – 1 is not positive.
(ii) ~q: There exists a cat which does not scratch.
(iii) ~r: There exists a real number x such that neither x > 1 nor x < 1.
(iv) ~s: There does not exists a number x such that 0 < x < 1.
(ii) ~q: There exists a cat which does not scratch.
(iii) ~r: There exists a real number x such that neither x > 1 nor x < 1.
(iv) ~s: There does not exists a number x such that 0 < x < 1.
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