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

Mathematics serves more than simply academic purposes. Students who want to succeed in life must identify their mission. In general, Mathematics is used in every aspect of life. In today’s world, firms require quantifiable input and output for performance evaluation Students should study Mathematics properly to have a fruitful career ahead.

Students should have good mathematical reasoning capabilities. A crucial ability that allows students to assess a given hypothesis without referring to a specific context or meaning is known as mathematical reasoning. The reasoning is not based on an individual’s opinion when a scientific investigation or assertion is investigated, to put it simply. A factual and scientific foundation is required for derivations and proofs. Students who wish to add value to the table must practise NCERT Solutions.

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

On the other side, mathematical reasoning aids in the development of logical reasoning and critical thinking in Mathematics. Inadequate mathematical thinking abilities can affect performance not only in Mathematics but also in Physics, Chemistry, and Economics.

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The most fundamental and vital tool in Mathematics is reasoning. It aids in comprehending and defending mathematical theorems. Students will be better able to apply the concepts they learn in class if they have a strong grasp of reasoning. The NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 consists of crucial ideas and formulas that will help students revise the basic topics while also being able to refer to the solutions of Class 11 Maths Chapter 14 Exercise 14.2.

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Extramarks assists students with their homework by providing chapter-by-chapter solutions for all classes, such as the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2.The NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 not only help with the mathematical problems but also give an insight into how the question papers might be framed for the final examinations. To improve their grades and gain confidence, students should consult the NCERT Solutions for Class 11 Maths, Chapter 14, Exercise 14.2.On  Extramarks’ website and mobile application, students can download the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 that have been created by qualified Mathematics teachers at Extramarks following the CBSE (NCERT) books’ criteria. Extramarks’ NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 are recommended for students to download as they will help them review the entire syllabus and score higher exam marks.

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

This Extramarks website contains the subject-matter experts’ NCERT Solutions For Class 11 Maths Chapter 14 Exercise 14.2 of mathematical reasoning. The PDF provided by Extramarks offers solutions to a majority of the exercises from the textbook, allowing students to put the ideas together for the test and do well on it. The NCERT Solutions are straightforward and easy to understand. A student in Class 11 can accurately comprehend the idea of mathematical reasoning thanks to these solutions. The questions in Class 11 Maths Chapter 14 Exercise 14.2 are crucial for performing well in the Class 11 final examinations.

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NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 for Math Compound assertions serve as the foundation for mathematical reasoning. A statement that is composed of two or more other statements is known as a compound statement. Additionally, the topic of subtracting new assertions from existing ones and negating statements is covered. The questions, sample problems, examples, and illustrations in the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 effectively teach this subject.

This exercise includes three problems that require students to write the negations and compound statements of the supplied sentences. Students can quickly master the logic to infer compound statements from two statements by practising these problems. Such abilities are very helpful in answering logical connectivities-based issues, which are frequently posed in various competitive tests. Students can download a scrollable PDF version of NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 from the Extramarks’ website and mobile application.

Experts at Extramarks, have created the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 in an easy-to-understand format to encourage effective Mathematics learning. For students to master this chapter, solving sample problems and the illustrations offered in the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 is quite beneficial. Students should concentrate more on removing uncertainties and developing logic since it is a fundamental subject matter.

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The NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 provide students with an elaborative understanding of the topic, allowing them to easily solve the question and all the problems.The NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 have been prepared following the guidelines of the CBSE. Students can benefit from the thorough study materials that Extramarks offers. They can concentrate on developing a more effective preparation strategy because there are five units. The 3D movies offered by Extramarks will make learning entertaining for students. To begin practising for the final examination, students can refer to the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2.

Statements, Logical Connectives, Quantifiers, Implications, and Validating Statements are the subtopics of NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2.

Since the results of the Class 11 exams will have a significant impact on the future, students must prepare diligently. They must follow the current CBSE curriculum and practise extensively with the help of the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2. Students who do well in Class 11 will have no trouble passing the Class 12 exams. Students should therefore put a lot of effort into practising the NCERT Solutions like the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2.

For the upcoming academic year 2022–2023, NCERT Solutions for Class 11 Math Chapter 14 Exercise 14.2 of Mathematical Reasoning are available for download in PDF format on the Extramarks’ website.

NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 (Ex 14.2) and all NCERT Solutions at one location, produced by qualified teachers, are in accordance with NCERT (CBSE) book rules and are available to download in PDF format. Students can use the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 to review the entire syllabus and earn higher grades.

For CBSE students preparing for exams, using the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 is thought to be the best option. There are numerous exercises in this chapter. The NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 are available on Extramarks’ website in PDF format. Students have the option of studying these solutions straight from Extramarks’ website or mobile application, or downloading them according to their convenience.The NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 can be relied upon during the final exam preparation.

The problems and questions from the NCERT Solutions for Class 11 Math Chapter 14 Exercise 14.2 have been meticulously compiled by the subject matter experts at Extramarks adhering to all CBSE requirements. Class 11 students can easily score higher on the final exam if they are familiar with all the ideas from the textbook and are good at solving all the problems from the exercises included in it. Students may quickly understand the types of questions that could be asked in the exam from this chapter and learn the chapter by using the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2 so that they can adequately study for the final exam.

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

In NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2, students will study some fundamentals of deductive reasoning as well as some fundamentals of mathematical reasoning.The NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.2  covers the following topics:

• Statements
• New statements from old
• Negation of a statement
• Compound statements
• Special words/phrases
• The word “And”
• The word “Or”
• Quantifiers
• Implications
• Contrapositive and converse
• Validating statements

Chapter-wise List of the NCERT Solutions for Mathematics provided by Extramarks:

• Chapter 1 – Sets

Sets are the topic of Chapter 1 of the CBSE Class 11 Mathematics textbook. Class 11 students should attentively follow the subtopics. An excellent strategy to get ready for exams is to use the NCERT Solutions for Class 11 Maths Chapter 1. It will be simpler for examinees to practise these as they are already familiar with Sets. Extramarks offers students more than 500 questions drawn from the top 50+ textbooks. These practise questions are all accessible for review, which will be very helpful for students. Examinable practise with the NCERT Solutions for Class 11 Maths Chapter 1 is essential.Workflow increases once students begin to practise these problems. Students will therefore have the choice to easily study for exams.

In Chapter 1 of the NCERT textbook, the concepts of functions and relations are defined using sets. NCERT Class 11 Maths Chapter 1 comprises some basic set-related concepts and operations. It is essential to gain a fundamental understanding of Sets since it is necessary for the study of Sequences, Geometry, and Probability.

Students in Class 11 must make sure they adequately prepare for the exam. Making use of Extramarks’ study resources can be very beneficial. Students can also consult these to understand concepts better. While studying for the test, the NCERT Solutions, Exemplars, 3D films, and Explainer videos are helpful. This enables the students to concentrate on specifics and practise well.

• Chapter 2 – Relations and Functions

Mathematical professionals with years of expertise have created the NCERT solutions for Class 11 Math Chapter 2. The Extramarks faculty takes great delight in creating study guides, crucial questions, mock exams, and other resources to aid students in getting ready for board exams. Students can get the class 11 Math Chapter 2 activity and answers from this article.

Sets, subsets, relationships between quantities, numbers, algebraic identities, and other topics are covered in Relations and Functions. Along with discussing the connections between each subject and their applications, the chapter also covers the ideas of domain, range, and functions.

Q.1 Write the negation of the following statements:

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

$\sqrt{2}\text{\hspace{0.17em}}\mathrm{is}\text{}\mathrm{not}\text{}\mathrm{a}\text{}\mathrm{complex}\text{}\mathrm{number}.$

(iii) All triangles are not equilateral triangle.
(iv) The number 2 is greater than 7.
(v) Every natural number is an integer.

Ans.
(i) Negation: Chennai is not the capital of Tamil Nadu.
(ii) Negation:

$\sqrt{2}\text{\hspace{0.17em}}\mathrm{is}\text{}\mathrm{a}\text{}\mathrm{complex}\text{}\mathrm{number}.$

(iii) Negation: All triangles are equilateral triangles.
(iv) Negation: The number 2 is not greater than 7.
(v) Negation: Every natural number is not an integer.

Q.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.

Ans.
(i) The negation of the given statement is “The number x is a rational number.”
And if a number is not a rational number it means that number is a rational number.
Thus, the given statements are negation of each other.

(ii) The negation of “The number x is a rational number” is “The number x is a irrational number”, which is same as second statement.
Thus, the given statements are negation of each other.

Q.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.

Ans.
(i) The component statements are:
p: Number 3 is prime.
q: Number 3 is odd.
Both statements p and q are true.

(ii) The component statements are:
p: All integers are positive.
q: All integers are negative.
Both 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.
Statements p and q are false. Statement r is true.

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