NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Exercise 14.2
If you are searching for NCERT Solutions of Chapter 14 Mathematical Reasoning Exercise 14.2 then you can find them here. NCERT Solutions of Class 11 Maths will cover all the basic details of the chapter so you can practice the questions and get all concept provided in the chapter. These will be helpful in boosting your marks in the examinations.
1. Write the negation of the given statements:
(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.
Answer
(i) Chennai is not the capital of Tamil Nadu.
(ii) √2 is a complex number.
(iii) All triangles are equilateral triangles.
(iv) The number 2 is not greater than 7.
(v) Every natural number is not an integer.
2. Are the following pairs of statements negations of each other:
(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.
Answer
(i) The negation of the first statement is “the number x is a rational number”. Which is the same as the second statement. This is because if that the number is not irrational, it is a rational. Therefore, the given pairs are negations of each other.
(ii) The negation of the first statement is “x is an irrational number” which is the same as the second statement. Therefore, the pairs are negations of each other.
3. Find the component statements of the following compound statements and check whether they are true or false.
(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.
Answer
(i) p: The number 3 is prime.
q: The number 3 is odd.
p, q are connected by or it is true.
(ii) p: All integers are positive.
q: All integers are negative.
p, q are connected by the word or p and q both are false.
(iii) p: 100 is divisible by 3
q: 100 is divisible by 11
q: 100 is divisible by 5
p is false, q is false, r is true
p and q and r is a false statement.
q: The number 3 is odd.
p, q are connected by or it is true.
(ii) p: All integers are positive.
q: All integers are negative.
p, q are connected by the word or p and q both are false.
(iii) p: 100 is divisible by 3
q: 100 is divisible by 11
q: 100 is divisible by 5
p is false, q is false, r is true
p and q and r is a false statement.