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 : 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.

Answer 1

(i) ~p : There exists a positive real number x such that x - 1 is not positive.

(ii) ~q : There exist 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 exist a number x such that 0 < x < 1.