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

Answer 1

(i) The negation of statement p is as follows.

There exists a positive real number x, such that x – 1 is not positive.

(ii)The negation of statement q is as follows.

There exists a cat that does not scratch.

(iii) The negation of statement r is as follows.

There exists a real number x, such that neither x > 1 nor x < 1.

(iv) The negation of statement * is as follows. There does not exist a number x, such that 0 < x < 1.