12.

Write the negation of the following statements and check whether the resulting statements are true,

(i) There does not exist a quadrilateral which has all its sides equal.

(ii) The sum of 3 and 4 is 9.

(iii) Australia is a continent.

(iv) Every natural number is greater than 0. 

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. 

Write the negation of the following statements:

(i) New Delhi is a city.                    

 (ii) The sky is blue.

(iii) The sum of the angles of a triangle is equal to two right angles.

(iv) Kavita is a hard working girl. 

(v) Two plus two is equal to 6.

Write the negation of the following statements.

(i) p : For every real number x, x² > x.

(ii) q : There exists a rational number x such that x² = 2

(iii) r : All birds have wings.

(iv) s : All students study Mathematics at the elementary level.