Chapter 14 : Mathematical Reasoning

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(i) There are 35 days in a month

(ii) Mathematics is difficult

(iii) The sum of 5 and 7 is greater than 10

(iv) The square of a number is an even number

(v) The sides of a quadrilateral have equal length

(vi) Answer this question

(vii) The product of (−1) and 8 is 8

(viii) The sum of all interior angles of a triangle is 180∘

(ix) Today is a windy day

(x) All real numbers are complex numbers

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(i) The number x is not a rational number

The number x is not an irrational number

(ii) The number x is a rational number

The number x is an irrational number

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(i) Number 3 is prime or it is odd

(ii) All integers are positive or negative

(iii)100 is divisible by 3, 11 and 5

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(i) Chennai is the capital of Tamil Nadu

(ii) √2 is not a complex number

(iii) All triangles are not equilateral triangle

(iv) The number 2 is greater than 7

(v) Every natural number is an integer

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(i) There exists a number which is equal to its square

(ii) For every real number x, x is less than x+1

(iii) There exists a capital for every state in India

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(i) x+y=y+x is true for every real numbers x and y

(ii) There exists real number x and y for which x+y=y+x

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(i) All rational numbers are real and all real numbers are not complex

(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

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(i) Sun rises or Moon sets

(ii) To apply for a driving licence you should have a ration card or a passport

(iii) All integers are positive or negative

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If a natural number is odd then its square is also odd.

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(a) If you live in Delhi then you have winter clothes

(i) If you do not have winter clothes then you do not live in Delhi

(ii) If you have winter clothes then you live in Delhi

(b) If a quadrilateral is a parallelogram then its diagonals bisect each other

(i) If the diagonals of a quadrilateral do not bisect each other then the quadrilateral is not a parallelogram

(ii) If the diagonals of a quadrilateral bisect each other then it is a parallelogram

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(i) You get a job implies that your credentials are good

(ii) The Banana trees will bloom if it stays warm for a month

(iii) A quadrilateral is a parallelogram if its diagonals bisect each other

(iv) To get A+ in the class it is necessary that you do the exercises of the book

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(i) If x is a prime number then x is odd

(ii) It the two lines are parallel then they do not intersect in the same plane

(iii) Something is cold implies that it has low temperature

(iv) You cannot comprehend geometry if you do not know how to reason deductively

(v) x is an even number implies that x is divisible by 4

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p : If x is an integer and x2 is even then x is also even

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(i) p : Each radius of a circle is a chord of the circle

(ii) q : The centre of a circle bisects each chord of the circle

(iii) r : Circle is a particular case of an ellipse

(iv) s : If x and y are integers such that x>y then −x<−y

(v) t : √11 is a rational number

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p : "If x is a real number such that x3+4x=0 then x is 0" is true by

(i) direct method

(ii) method of contradiction

(iii) method of contrapositive

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(i) p : If all the angles of a triangle are equal then the triangle is an obtuse angled triangle.

(ii) q : The equation x2−1 =0 does not have a root lying between 0 and 2.

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(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<x<1

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(i) p : A positive integer is prime only if it has no divisors other than 1 and itself

(ii) q : I go to a beach whenever it is a sunny day

(iii) r : If it is hot outside then you feel thirsty

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