NCERT class 11 maths chapter 14 Mathematical Reasoning
Question 1: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.
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Question 2:State the converse and contrapositive of each of the following statements: (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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Question 3:Write each of the statements in the form “if p, then q” (i) p: It is necessary to have a password to log on to the server. (ii) q: There is traffic jam whenever it rains. (iii) r: You can access the website only if you pay a subsciption fee.
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Question 4:Rewrite each of the following statements in the form “p if and only if q” (i) p: If you watch television, then your mind is free and if your mind is free, then you watch television. (ii) q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly. (iii) r: If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.
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Question 5:Given below are two statements p : 25 is a multiple of 5. q : 25 is a multiple of 8. Write the compound statements connecting these two statements with “And” and “Or”. In both cases check the validity of the compound statement.
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Question 6:Check the validity of the statements given below by the method given against it. (i) p: The sum of an irrational number and a rational number is irrational (by contradiction method). (ii) q: If n is a real number with n > 3, then n2 > 9 (by contradiction method).
Question 7:Write the following statement in five different ways, conveying the same meaning. p: If a triangle is equiangular, then it is an obtuse angled triangle.
