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

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 11 |

Subject | Maths |

Chapter | Chapter 14 |

Exercise | Class 11 Maths Chapter 14 Mathematical Reasoning Exercise 14.2 |

Number of Questions Solved | 3 |

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

**NCERT TEXTBOOK EXERCISES**

**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 statement is: Chennai is not the capital of Tamil Nadu.**(ii)** Negation of statement is: √2 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.

**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 r is true.

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

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