**NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex
14.2**

NCERT Solutions for Class
11 Maths Chapter 14
Mathematical Reasoning Ex 14.2 are the part of NCERT Solutions for Class 11
Maths. Here you can find the NCERT Solutions for Class 11 Maths Chapter 14
Mathematical Reasoning Ex 14.2.

**Ex 14.2
Class 11 Maths Question 1.**

Write the negation of the following 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.

**Solution:**

**(i)** Negation of the statement: Chennai is not the capital of Tamil
Nadu.

**(ii)** Negation of the statement: √2 is a complex
number.

**(iii)** Negation of the statement: All triangles are equilateral
triangles.

**(iv)** Negation of the statement: The number 2 is not greater than 7.

**(v)** Negation of the statement: Every natural number is not an
integer.

**Ex 14.2 Class 11 Maths Question 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.

**Solution:**

**(i)** Let p: The number x is not a rational number.

q: The number x is not an irrational number.

Now, ~p: The number x is a rational number. ~q: The number x is an irrational
number.

∴ ~p = q and ~q = p

Thus, p and q are negations of each other.

**(ii)** Let p: The number x is a rational number.

q: The number x is an irrational number.

Now, ~p: The number x is not a rational number.

~q: The number x is not an irrational number.

∴ ~p = q and ~q = p

Thus, p and q are negations of each other.

**Ex 14.2 Class 11 Maths Question 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.

**Solution:**

**(i)** The component statements are:

p: Number 3 is prime.

q: Number 3 is odd.

Both the component statements p and q are true.

**(ii)** The component statements are:

p: All integers are positive.

q: All integers are negative.

Both the component statements p and q are false.

**(iii)** The component statements are:

p: 100 is divisible by 3.

q: 100 is divisible by 11.

r: 100 is divisible by 5.

The component statements p and q are false whereas the component statement r is
true.

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