Accessing ISC Mathematics Class 11 OP Malhotra Solutions Chapter 27 Mathematical Reasoning Ex 27(b) can be a valuable tool for students seeking extra practice.
S Chand Class 11 ICSE Maths Solutions Chapter 27 Mathematical Reasoning Ex 27(b)
Question 1.
Identify the quantifier in the following statements.
(i) There exists a capital city for every state of India.
(ii) For every real numbers, x is less than x + 1.
(iii) At least one natural number is not a prime number.
Solution:
(i) There exists.
(ii) For every.
(iii) Atleast.
Question 2.
Symbolise the following statements.
(i) There is at least one number in the set of natural numbers which is equal to ‘its’ cube.
(ii) The square of every real number is positive.
(iii) There exists at least one number in A = {5, 7, 8, 9, 10} which is an even number.
(iv) For every real number x, x < x + 1.
(v) The square roots of all prime numbers are irrational numbers. (Let P denote the set of prime numbers and Q that of irrational numbers).
Solution:
(i) ∃ x ∈ N s.t x = x3
since 1 e N and 1 = 13
(ii) ∀ x ∈ R s.tx2 > 0
(iii) ∃ x ∈ A s.t x is even, since 8, 10 ∈ A
(iv) ∀ x ∈ R, x < x + 1, since successor of every real number is greater than itself.
(v) ∀ x ∈ P, √x ∈ Q