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Question

Write the negation of the following statements:
(i) p : For every positive real number x, the number (x − 1) is also positive.
(ii) q : For every real number x, either x > 1 or x < 1.
(iii) r : There exists a number x such that 0 < x < 1.


Solution

(i) p: For every positive real number x, the number (x − 1) is also positive.
 ~p: At least for one positive real number x, the number (x-1) is not positive.

(ii) 
q: For every real number x, either x > 1 or x < 1.
 ~q: At least for one real number x, neither x > 1 nor x < 1.

(iii) 
r: There exists a number x such that 0 < x < 1.
   ~r: For every real number x, either x  0 or x < 1
.

Mathematics
RD Sharma XI (2015)
Standard XI

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