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

NCERT Solutions for Class 11 Maths Chapter 14 ensure that all your doubts are explained in the most comprehensive format. Chapter 14** **is divided into 6 parts. The main topics of the chapter ae statements, new statements from the old, negation of a statement, compound statements, special words/phrases, the word “And”, the word “Or”, quantifiers, implications, contrapositive and converse, validating statements by contradiction.

NCERT Solutions for Class 11 Maths Chapter 14 consists of 6 exercises in total. The nature of the questions varies from exercise to exercise. Solutions to all chapter-end exercises are provided in order to ensure that all the aspects of the chapter are covered in detail. These solutions will make it easier for you to comprehend the concepts of the chapter. All the solutions are based on the CBSE class 11 maths syllabus.

## Important Topics of NCERT Solutions for Class 11 Maths Chapter 14

NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning is one of the significant chapters from the exam’s perspective. It is important to continuously practice your concepts in order to attain the perfect score. To begin, there are two types of reasoning, namely, inductive and deductive reasoning. Some important terms in Mathematical Reasoning are as follows:

**Statement**

A sentence is called a statement if it is either true or false. If a sentence is both true and false, it is not a statement. A true statement is called a valid statement and a false statement is called an invalid statement. A statement should be one that is mathematically acceptable.

**Logic**

Logic refers to the methodology used for reasoning and it also helps in determining the validity of an argument

**Open and Compound Statement**

An open statement consists of one or more variables that are assigned certain values. Compound statements are made up of the two or more simple statements. Compound statements are formed with the use of connecting words such as “And”, “Or”, “Not”, “If”, etc. Or consists of two types- exclusive “or” and inclusive “or”.

**Elementary of Operations of Logic**

Elementary operations of logic consist of Conjunction, Disjunction, Negation, Conditional and Biconditional Sentences. Conjunction refers to a compound sentence being formed using the connective “and”. Disjunction forms compound sentences using the connective “or”.

Negation changes the truth value of a statement with the help of words like “no” or “not”. When two simple sentences are connected by “if” and “then” they are conditional sentences. Biconditional sentences connect two simple sentences with the phrase “if” and “only”.

**Truth Value**Any given statement can either be termed as true or false. These are truth values of a statement which are represented by “T” and “F”.

### Exercise-Wise Discussion of NCERT Solutions for Class 11 Maths Chapter 14

**NCERT Solutions for Class 11**Maths Chapter 14 consists of 6 exercises, out of which one exercise is a miscellaneous exercise.- Exercise 14.1 consists of 2 questions. The first question asks you to identify which sentences are statements and the second asks you to give examples of sentences that are not statements.
- Exercise 14.2 consists of 3 questions. This exercise deals with negations.
- Exercise 14.3 consists of 4 questions and deals with quantifiers and the use of “or”.
- Exercise 14.4 also consists of 4 questions. This exercise encircles topics such as “if-then” and contrapositives.
- Exercise 14.5 has 5 questions that ask you to show statements by the direct method, method of contradiction, method of contrapositive. You’ll also be asked to state which questions are true or false.
- The miscellaneous exercise consists of 7 questions that summarize the entire chapter. Questions asked here cover most of the important concepts.

### Benefits of NCERT Solutions for Class 11 Maths Chapter 14 by Instasolv

NCERT Solutions for Class 11 Maths are created by the best math teachers at Instasolv. They understand CBSE guidelines and exam pattern and hence design the solutions accordingly. All the solutions are solved step by step so as to avoid any confusion.

To conclude, Mathematical Reasoning NCERT Solutions for Class 11 by Instasolv is a self-sufficient guide that you need to solve all your queries related to the chapter. The solutions provided in this guide will pinpoint what the subject demands from you and help you understand the areas you need to work on in order to improve your understanding of the subject.