# NCERT Solutions For Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3

Here, Below you all know about NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3 Question Answer. I know many of you confuse about finding Chapter 14 Mathematical Reasoning Ex 14.3 Of Class 11 NCERT Solutions. So, Read the full post below and get your solutions.

Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 11 |

Subject | Maths |

Chapter | Chapter 14 |

Exercise | Class 11 Maths Chapter 14 Mathematical Reasoning Exercise 14.3 |

Number of Questions Solved | 4 |

## NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3

**NCERT TEXTBOOK EXERCISES**

**Ex 14.3 Class 11 Maths Question 1.**

For each of the following compound statements first, identify the connecting words and then break it into component statements.

**(i)** All rational numbers are real and all real numbers are not complex.**(ii)** Square of an integer is positive or negative.**(iii)** The sand heats up quickly in the Sun and does not cool down fast at night.**(iv)** x = 2 and x = 3 are the roots of the equation 3x^{2} β x β 10 = 0.

**Solution:**

**(i)** The compound statement has the connecting word βandβ. Component statements are

p: All rational numbers are real.

q: All real numbers are not complex.

**(ii)** The compound statement has the connecting word βorβ. Component statements are:

p: Square of an integer is positive.

q: Square of an integer is negative.

**(iii)** The compound statement has the connecting word βandβ. Component statements are:

p: The sand heats up quickly in the sun.

q: The sand does not cool down fast at night.

**(iv)** The compound statement has the connecting word βandβ. Component statements are:

p: x- 2 is a root of the equation 3x^{2} β x β 10 = 0.

q: x = 3 is a root of the equation 3x^{2} β x β 10 = 0.

**Ex 14.3 Class 11 Maths Question 2.**

Identify the quantifier in the following statements and write the negation of the statements.

**(i)** There exists a number which is equal to its square.**(ii) **For every real number x, x is less than x + 1.**(iii)** There exists a capital for every state in India.

**Solution:**

**(i)** Here the quantifier is βthere existsβ.

The negation of statement is: There does not exist a number which is equal to its square.**(ii)** Here the quantifier is βfor everyβ

The negation of statement is: For at least one real number x, x is not less than x + 1.**(iii)** Here the quantifier is βthere existsβ

The negation of statement is: There exists a state in India which does not have a capital.

**Ex 14.3 Class 11 Maths Question 3.**

Check whether the following pair of statements is negation of each other. Give reasons for your answer.

**(i)** x + y = y + x is true for every real numbers x and y.**(ii)** There exists real numbers x and y for which x + y = y + x.

**Solution:**

Let p: x + y = y + x is true for every real numbers x and y.

q: There exists real numbers x and y for which

x+y=y + x.

Now, ~p: There exists real numbers x and y for which x + y β y + x.

Thus, ~p β q.

**Ex 14.3 Class 11 Maths Question 4.**

State whether the βOrβ used in the following statements is βexclusiveβ or βinclusiveβ. Give reasons for your answer.

**(i)** Sunrises or Moon sets.**(ii)** To apply for a driving license, you should have a ration card or a passport.**(iii)** All integers are positive or negative.

**Solution:**

**(i)** This statement makes use of exclusive βorβ. Since when sun rises, moon does not set during day-time.**(ii)** This statement makes use of inclusive βorβ. Since you can apply for a driving license even if you have a ration card as well as a passport.**(iii)** This statement makes use of exclusive βorβ. Since a integer is either positive or negative, it cannot be both.

## NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Exercise 14.3 PDF

For NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3, you may click on the link below and get your NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Exercise pdf file.

Finally, You all know about NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.3. If you have any questions, then comment below and share this post with others.