Short Answer TypeThe statement means that in every rectangle, both the diagonals have the same length.
The negation of this statement is ‘It is false that both the diagonals in a rectangle have the same length’. It means that there is at least one rectangle in which both the diagonals do not have the same length.
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.
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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