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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) The negation of the statement :

p : For every positive real number x, the number (x - 1) is also positive.

is

~p : There exists a positive real number x, such that the number (x -1) is also positive.

(ii) The negation of the statement :

q : For every real number x, either x > 1 or x < 1.

is

~q: There exists a real number such that neither x >1 or x < 1.

(iii)  The negation of the statement :

r : There exists a number  x such that 0 < x < 1.

is

~r: For every real number x , either x or x1.


Mathematics
RD Sharma
Standard XI

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