Class XI Chapter 14 – Mathematical Reasoning Maths ______________________________________________________________________________ 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 â€œ and â€ and â€œ Or â€. In both cases check the validity of the compound statement. Solution 5: The compound statement with ‘And’ is â€œ25 is a multiple of 5 and 8â€. This is a false statement, since 25 is not a multiple of 8. The compound statement with ‘Or’ is â€œ25 is a multiple of 5 or 8â€. This is a true statement, since 25 is not a multiple of 8 but it is a multiple of 5. 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 2 n > 9 (by contradiction method). Solution 6: (i) The given statement is as follows. p: the sum of an irrational number and a rational number is irrational. Let us assume that the given statement, p, is false. That is, we assume that the sum of an irrational number and a rational number is rational. b d Therefore, a , when a is irrational and b, c, d, e are integers. c e d b is a rational number and a is an irrational number. e c This is a contradiction. Therefore, our assumption is wrong. Therefore, the sum of an irrational number and a rational number is rational. Thus, the given statement is true. (ii)The given statement, q is as follows. 2 If n is a real number with n > 3, then n > 9. Let us assume that n is a real number with n > 3, but 2 That is, n < 9 Then, n > 3 and n is a real number. Squaring both the sides, we obtain 2 n > 3 2 2 n > 9 is not true. 2 2 n > 9, which is a contradiction, since we have assumed that n < 9. Thus, the given statement is true. That is, if n is a real number with n > 3, then 2 n > 9. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 14 – Mathematical Reasoning Maths ______________________________________________________________________________ Question 7: Write the following statement in five different ways, conveying the same meaning. P: If triangle is equiangular, then it is an obtuse angled triangle. Solution 7: The given statement can be written in five different ways as follows. (i)A triangle is equiangular implies that is an obtuse-angled triangle. (ii)A triangle is equilateral only if it an obtuse-angled triangle. (iii)For a triangle to be equiangular, it is necessary that the triangle is an obtuse-angled triangle. (iv)For a triangle to be an obtuse-angled triangle, it is sufficient that the triangle is equiangular. (v)If a triangle is not an obtuse-angled triangle, then the triangle is not equiangular. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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