Q4 of 18 Page 13

Are the following pairs of statements negations of each other:

(a) The number x is not a rational number. The number x is not an irrational number.

(b) The number x is a rational number. The number x is an irrational number.


(a) The negation of the first statement is "the number x is not rational number" which is same as the second statement. This is because if that number is not irrational then it is rational.

(b) The negation of the first statement is " x is an irrational number" which is same as the second statement. Therefore the pairs are negations of each other.

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(ii) is not a complex number

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(iv) The number 2 is greater than 7.

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(ii) Square of an integer is positive or negative.

(iii) The sand heats up quickly in the sun and does not cool down fast at night.

(iv) x = 2 and x = 3 are the roots of the equation 3x2 – x – 10 = 0.