## Mathematical Reasoning |

# Mathematical Reasoning NCERT Solutions Class 11 Maths Chapter 14 Exercise 14.1 14.2 14.3 14.4 14.5 Miscellaneous Free pdf Notes Study Material download-Anand Classes

NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning deals with the most basic math concepts based on logic and reasoning. The mental ability to reason is one of the most important assets of the human brain that makes it superior to other species. This chapter elaborates the process of mathematical reasoning. There are basically two types of reasoning– inductive and deductive. Inductive reasoning is a generalization based on observation whereas deductive reasoning is a hypothesis of whether a statement is true or false under specific conditions.

# Download the pdf of NCERT Solutions for Class 11 Maths Chapter 14 – Mathematical Reasoning

# Download the NCERT Book for Class 11 Maths Chapter 14 – Mathematical Reasoning

# Number of questions in each exercise of NCERT Solutions for Class 11 Maths Chapter 14 – Mathematical Reasoning

The basic applications of deductive reasoning involve geometrical and mathematical proofs. Thus, learning Mathematical Reasoning is crucial for studying other math topics. By using the NCERT Solutions Class 11 Maths Chapter 14, students will get well-versed with this topic and its applications in real-world situations. The sample questions and exercises provided in these solutions offer a step-by-step understanding of each topic. With the regular practice of Class 11 Maths NCERT Solutions Chapter 14, students will easily attain the knowledge to work on Mathematical Reasoning problems. To learn and practice with NCERT Solutions Chapter 14 Mathematical Reasoning, download the exercises provided in the links below.

- NCERT Solutions Class 11 Maths Chapter 14 Ex 14.1
- NCERT Solutions Class 11 Maths Chapter 14 Ex 14.2
- NCERT Solutions Class 11 Maths Chapter 14 Ex 14.3
- NCERT Solutions Class 11 Maths Chapter 14 Ex 14.4
- NCERT Solutions Class 11 Maths Chapter 14 Ex 14.5
- NCERT Solutions Class 11 Maths Chapter 14 Miscellaneous Exercise

Aristotle (384 B.C.-322 B.C.) was the first to write a treatise on logic. His study was based on the collection of rules for deductive reasoning which served as a basis for other branches. Another German mathematician named G. W. Leibnitz in the seventh century introduced the symbols in logic. In the nineteenth century, the English mathematician George Boole(1815–1864) and Augustus De Morgan (1806–1871), founded the modern subject of symbolic logic. NCERT solutions Class 11 Maths Chapter 14 Mathematical Reasoning are comprehensive guides that efficiently impart the understanding of this topic. These resources are competent to strengthen the logic required to study deductive reasoning.

The topic of Mathematical Reasoning may seem a little confusing to students when it comes to validating statements. Therefore, it is necessary to establish a clear and precise knowledge of this topic through practice. NCERT Solutions for Class 11 Maths Chapter 14 are well-framed after deep research to encourage in-depth learning of this topic. These resources are carefully formulated to support and enhance deductive reasoning in students. To practice with these solutions, click on the links of the pdf files given below

- Class 11 Maths Chapter 14 Ex 14.1 – 2 Questions
- Class 11 Maths Chapter 14 Ex 14.2 – 3 Questions
- Class 11 Maths Chapter 14 Ex 14.3 – 4 Questions
- Class 11 Maths Chapter 14 Ex 14.4 – 4 Questions
- Class 11 Maths Chapter 14 Ex 14.5 – 5 Questions
- Class 11 Maths Chapter 14 Miscellaneous Ex – 7 Questions

# Important Topics and Subtopics of NCERT Solutions for Class 11 Maths Chapter 14 – Mathematical Reasoning

**Topics Covered:** NCERT solutions Class 11 Maths Chapter 14 briefly introduces mathematical reasoning, its representation, and applications. The important topics covered in these solutions are understanding statements, deriving new statements from old ones, use of special words/phrases, implications, and validation of statements.

**Total Questions:** Class 11 Maths Chapter 14 Mathematical Reasoning has 25 questions in 6 exercises that are primarily based on evaluating mathematical statements, their logical connectivity, implications, and mathematical reasoning.

# List of Formulas in NCERT Solutions Class 11 Maths Chapter 14 – Mathematical Reasoning

Understanding concepts is a sure shot way to gain a clear understanding of a topic. This chapter does not consist of any formulas rather it simulates a child’s mathematical acumen. students have to use logic to draw sensible conclusions. NCERT Solutions Class 11 Maths Chapter 14 will help students gain deep knowledge of all topics with ease. Some of the important terms, formulas, and concepts related to Mathematical Reasoning explained in these solutions are listed below:

**Mathematical Reasoning:**Mathematical reasoning is a critical skill that enables students to analyze a given hypothesis without any reference to a particular context or meaning.

**Statements:**A sentence is called a mathematically acceptable statement if it is either true or false but not both.

**Compound statement:**A compound statement is a statement made up of two or more smaller statements called component statements of the compound statement.

**Deductive Reasoning:**Deductive reasoning, also deductive logic, is the process of reasoning from one or more statements (premises) to reach a logical conclusion.

## A Few Points on Chapter 14 Mathematical Reasoning

- A mathematically acceptable statement is a sentence which is either true or false.
- The negation of a statement p: If p denotes a statement, then the negation of p is denoted by ∼p.
- A statement is a compound statement if it is made up of two or more smaller statements. The smaller statements are called component statements of the compound statement.
- The words “And”, “Or”, “There exists”, and “For every” exist in compound statements.
- The implications are “If ”, “only if ”, and “ if and only if ”.

- The contrapositive of a statement p ⇒ q is the statement ∼ q ⇒ ∼p. The converse of a statement p ⇒ q is the statement q ⇒ p. p ⇒ q together with its converse gives p if and only if q.
- The following methods are used to check the validity of statements: (i) direct method, (ii) contrapositive method, (iii) method of contradiction, and (iv) using a counter-example.

# FAQs on NCERT Solutions Class 11 Maths Chapter 14 – Mathematical Reasoning

**Q1**

### What is the Importance of NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning?

NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning are well-framed as per the latest CBSE syllabus to support efficient math learning. The sample problems and illustrations provided in these solutions are quite prominent to form a clear understanding of mathematical reasoning and its practical applications. The learning pattern of these solutions is apt to promote math proficiency in students. The thorough practice of these resources will ensure a good score in exams.

**Q2**

### What are the Important Topics Covered in NCERT Solutions Class 11 Maths Chapter 14?

The important topics covered in the NCERT Solutions Class 11 Maths Chapter 14 are deductive reasoning, statements, deriving new statements from old, using special words/phrases, implications, and validation of statements. Apart from these some important subtopics included in these solutions are compound statements, component statements, the role of AND and OR in compound statements, methods to verify statements including direct method, contrapositive method, contradiction method, and method of using a counterexample. With strategic learning of all these topics, students will attain a deep understanding of Mathematical Reasoning without much effort.

**Q3**

### Do I Need to Practice all Questions Provided in Class 11 Maths NCERT Solutions Mathematical Reasoning?

The examples and questions provided in NCERT Solutions Class 11 Maths Mathematical Reasoning are well-explained in a step-by-step process to facilitate crystal clear concept building. Students should solve all these questions to ascertain sufficient practice for exams. Mastering the core fundamentals also helps in revising comfortably during the last minutes. Moreover, it is an easy way to establish the core foundation for error-free math learning which is quite helpful in facing competitive exams.

**Q4**

### How Many Questions are there in Class 11 Maths NCERT Solutions Chapter 14 Mathematical Reasoning?

NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning has 18 questions in 5 exercises plus 17 questions in one miscellaneous exercise. Solving these simple sums based on mathematical reasoning is sufficient to develop a clear understanding of the important terms, methods, and concepts explained in this chapter. The well-curated format of solutions is perfect to follow the step-by-step math learning approach for mastering all key basics.

**Q5**

### What are the Important Formulas in NCERT Solutions Class 11 Maths Chapter 14?

NCERT Solutions Class 11 Maths Chapter 14 well explains the core fundamentals of Mathematical Reasoning. Some important concepts described in these solutions are related to applying deductive reasoning to validate statements, compound statements, their rules, qualifiers, implications, contrapositive, and converses. These topics are elaborated in the solutions with detailed examples and illustrations to help students learn them better. This chapter also focuses more on using logic, thus students need to thoroughly learn each concept to build a clear understanding of reasoning and its applications.

**Q6**

### Why Should I Practice NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning?

NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning is a comprehensive learning guide that offers a complete reference to the whole syllabus of this chapter. By using these resources students form a firm base for advancing in their respective fields for future studies. These solutions deliver the knowledge of topics in a lucid manner for students to grasp the most difficult concepts easily. The regular practice of these resources ensures higher success rates in annual exams as well as competitive exams.

**Q7**

### Write down the main topics of the NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning.

1. Introduction

2. Statements

3. New Statements from Old

4. Special Words/Phrases

5. Implications

6. Validating Statements.

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