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.
(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 s is as follows.
There does not exist a number x, such that 0 < x < 1.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.