Short Answer Type
Long Answer TypeWrite 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.
Short Answer TypeLong Answer TypeWrite 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) Here, p: For every positive real number x, the number x - 1 is also positive.
~p: It is false that for every positive real number x, the number x - 1 is also positive.
Or
~p: There exists a positive real number x such that x - 1 is not positive.
(ii), Here, q: All cats scratch.
~q: It is false that all cats scratch.
Or
~q: There exists a cat which does not scratch.
(iii) Here, r: For every real number x, either x>1 or x<1.
~r: It is false that for every real number x, either x>1 or x<1.
Or
~r: There exists a real number x such that neither x>1 nor x<1.
(iv) Here, s: There exists a number x such that 0<x<1.
~s: It is false that there exists a number x such that 0<x<1.
Or
~s: There does not exist a number x such that 0<x<1.
Short Answer TypeLong Answer TypeWrite 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.
is an irrational number. (ii) 
is an irrational number.
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