. 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 exist a number x such that 0 <  < 1

 

Best Answer

Explanation:

The negation of statement p is "not p." The negation of p is symbolized by " ~p.”  The truth value of  ~p pis the opposite of the truth value of p.

(i) ~ p: There exists at least one positive real number x for which x-1 is not positive.

(ii) ~ q: All cats do not scratch. or we may say that there is at least one cat which does not scratch.

(iii) ~r: There exists at least one number x such that neither x>1nor x<1.

(iv) ~ s: There does not exist a number such that 0<x<21.

Final Answer:

(i) ~ p: There exists at least one positive real number x for which x-1 is not positive.

(ii) ~ q: All cats do not scratch. or we may say that there is at least one cat which does not scratch.

(iii) ~r: There exists at least one number x such that neither x>1nor x<1.

(iv) ~ s: There does not exist a number such that 0<x<21.

Talk to Our counsellor