NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.2 are part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.2.

- Mathematical Reasoning Class 11 Ex 14.1
- Mathematical Reasoning Class 11 Ex 14.3
- Mathematical Reasoning Class 11 Ex 14.4
- Mathematical Reasoning Class 11 Ex 14.5

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 11 |

Subject |
Maths |

Chapter |
Chapter 14 |

Chapter Name |
Mathematical Reasoning |

Exercise |
Ex 14.2 |

Number of Questions Solved |
3 |

Category |
NCERT Solutions |

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

**Question 1.**

Write the negation of the following statements:

**(i)** Chennai is the capital of Tamil Nadu.

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

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

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

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

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

**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.

**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 r is true.

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