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 $\left(x-1\right)$ 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 nor . (iii) r: There exists a number x such that 0 < x < 1.    ~r: For every real number x, either or .MathematicsRD Sharma XI (2015)Standard XI

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