The NCERT Solution for Class 11 maths includes answers to every question from the NCERT text book’s exercise. Top students love SWC NCERT Solutions because they are very effective. In general, Class 11 is regarded as the most significant year in a student’s professional development. The NCERT answers for class 11 maths were created with the goal of providing students with the most help possible.

Answers to the class 11 maths questions provided in the exercise might be challenging for students for a number of reasons. One should not omit any NCERT textbook content in order to get the highest possible grade. Use the Swastik Classes’ NCERT answers for maths class 11 as a resource. Important exam-based questions are covered in depth in each chapter.

### NCERT Solutions for Class-11 Maths Exercise 14.3

**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} – x – 10 = 0.**

**Solution :**

(i) Here, the connecting word is ‘and’.

The component statements are as follows.

p: All rational numbers are real.

q: All real numbers are not complex.

(ii) Here, the connecting word is ‘or’.

The component statements are as follows.

p: Square of an integer is positive.

q: Square of an integer is negative.

(iii) Here, the connecting word is ‘and’.

The component statements are as follows.

p: The sand heats up quickly in the sun.

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

(iv) Here, the connecting word is ‘and’.

The component statements are as follows.

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

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

**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) The quantifier is “There exists”.

The negation of this statement is as follows.

There does not exist a number which is equal to its square.

(ii) The quantifier is “For every”.

The negation of this statement is as follows.

There exist a real number x such that x is not less than x + 1.

(iii) The quantifier is “There exists”.

The negation of this statement is as follows.

There exists a state in India which does not have a capital.

**Question****3. Check whether the following pair of statements is negation of each other. Give reasons for the answer.**

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

**(ii) There exists real number x and y for which x + y = y + x.**

**Solution :**

The negation of statement (i) is as follows.

There exists real number x and y for which x + y ≠ y + x. This is not the same as statement (ii).

Thus, the given statements are not the negation of each other.

**Question****4. State whether the “Or” used in the following statements is “exclusive “or” inclusive. Give reasons for your answer.**

**(i) Sun rises or Moon sets.**

**(ii) To apply for a driving licence, you should have a ration card or a passport. **

**(iii) All integers are positive or negative.**

**Solution :**

(i) Here, “or” is exclusive because it is not possible for the Sun to rise and the moon to set together.

(ii) Here, “or” is inclusive since a person can have both a ration card and a passport to apply for a driving licence.

(iii) Here, “or” is exclusive because all integers cannot be both positive and negative.

## Conclusions for NCERT SOLUTIONS FOR CLASS 11 MATHS CHAPTER 14-MATHEMATICAL REASONING EXERCISE 14.3

An academic team of knowledgeable members of SWC has produced and published the NCERT Solutions for class 11’s maths chapter for your use as a reference. You can get answers to all of the chapters of the NCERT maths class 11 here at SWC. Please make use of the following NCERT answers that were created by SWC as a reference for this chapter. In addition to that, study the chapter’s theory before attempting to solve the NCERT problems.