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`.

Explanation

(i) there exists a positive real number x such that `x-1` is not positive.
(ii) there exists at least one cat which does not scratch.
(iii) there exists a real number `x` such that neither `xgt1` nor `xlt1`.
(iv) For every real number `x,x le0`or `xge1`.