# NCERT Exemplar Class 11 Maths Chapter 14 Solutions: Mathematical Reasoning

NCERT Exemplar Solutions for Class 11 Maths Chapter 14 deals with the few basic concepts of mathematical reasoning. This chapter will make you understand how well you can use the power of reasoning. Some of the main topics of the chapter of NCERT Exemplar Class 11 Maths include the definition of statements, compound statements, simple statements, conjunctions, disjunction, negation, quantifiers, the conditional statement, validity of statements, and the bi-conditional statement.

NCERT Exemplar Problems and Solutions for Class 14 Maths consists of 2 main exercises and 55 questions. The main aim to provide these exemplar problems with solutions is to make you understand every concept clearly. All the solutions are prepared by the expert maths teachers at Instasolv. These solutions explain the steps with accuracy, without missing out on necessary parts of solving a question.

These NCERT Exemplar Problems with Solutions, prepared by experts at Instasolv, are a comprehensive study material for you to prepare for Class 11 exams. These have been arranged for years as a complete source of material to you, to develop your analytical skills. Also, these solutions are easily accessible online. You can follow them anytime and anywhere.

## Important Topics for NCERT Maths Exemplar Solutions Class 11 Chapter 14 – Mathematical Reasoning

**What is Mathematical Reasoning?**

There are two different kinds of reasoning available including:

- Inductive Reasoning
- Deductive Logic Reasoning

Logic is the study that is completed with the method of reasoning. Along with verifying the theorem, it offers us the rules for defining the validity of a certain argument.

**What is a Statement?**

The basic unit included in mathematical reasoning is considered as a mathematical statement. A statement is a positive sentence that is either true or false but not both a true statement is termed as a valid statement. Else, it is known as an invalid statement.

**The Negation of a Statement**

If p represents a statement, then the negation of p is represented by ∼p.

**Compound Statement**

If a statement is made up of two or smaller statements then it is said to be a compound statement. The smaller statements are known as component statements of the compound statement.

The Compound statements are prepared by:

- Connectives denoted by “AND”, “OR”
- Quantifiers denoted by “There exists”, “For every”
- Implications denoted by “If”, “only if”, “if and only if”.

**Denotation of Statement**

Statements are represented by the small letters i.e., a, b, c, d … etc.

Example:

- Maths is fun
- This sentence is subjective in the sense that for those who like maths, it may be fun but for others, it may not be. This deals with the fact that this sentence is not true at all times. Therefore, it is not a statement
- A statement should be considered as a “statistically acceptable” statement
- An uncertain sentence is not acceptable as a statement in maths.

**Methods to Check Validity**

We can use different methods to check the validity of a statement including:

- Direct Method
- Contrapositive method
- Methods using contradiction
- Methods using counterexample

### Exercise Discussion of NCERT Maths Exemplar Solutions Class 11 Chapter 14 – Mathematical Reasoning

NCERT Exemplar Class 11 for Maths Solutions of Chapter 14 – Mathematical Reasoning consists of solved examples as well as the exercises for practice. There are around 18 solved examples and 2 exercises which consist of a total of 37 questions. The description of these exercises are listed below:

**Exercise 14.1 – Short Answer Type Questions**

In this exercise of Chapter 14 – Mathematical Reasoning there are a total of 16 questions that are based on the basic concepts of mathematical reasoning.

**Exercise 14.2 – Objective Type Questions**

This exercise consists of a total of 21 questions which are objective type questions based on compound statements, simple statements, conjunctions, disjunction, negation, quantifiers, the conditional statement, validity of statements, and the bi-conditional statement. This exercise consists of very short answer questions including fill in the blanks, match the following, and state true or false type questions.

## Why Use NCERT Maths Exemplar Solutions Class 11 Chapter 14 – Mathematical Reasoning by Instasolv?

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