# NCERT Class 12 Mathematics Proofs In Mathematics

Read and download NCERT Class 12 Mathematics Proofs In Mathematics chapter in NCERT book for Class 12 Mathematics. You can download latest NCERT eBooks for 2021 chapter wise in PDF format free from Studiestoday.com. This Mathematics textbook for Class 12 is designed by NCERT and is very useful for students. Please also refer to the NCERT solutions for Class 12 Mathematics to understand the answers of the exercise questions given at the end of this chapter

## Proofs In Mathematics Class 12 Mathematics NCERT

Class 12 Mathematics students should refer to the following NCERT Book chapter Proofs In Mathematics in standard 12. This NCERT Book for Grade 12 Mathematics will be very useful for exams and help you to score good marks

### Proofs In Mathematics NCERT Class 12

A.1.1 Introduction
In Classes IX, X and XI, we have learnt about the concepts of a statement, compound statement, negation, converse and contrapositive of a statement; axioms, conjectures, theorems and deductive reasoning.

Here, we will discuss various methods of proving mathematical propositions.

A.1.2 What is a Proof?
Proof of a mathematical statement consists of sequence of statements, each statement being justified with a definition or an axiom or a proposition that is previously established by the method of deduction using only the allowed logical rules.

Thus, each proof is a chain of deductive arguments each of which has its premises and conclusions. Many a times, we prove a proposition directly from what is given in the proposition. But some times it is easier to prove an equivalent proposition rather than proving the proposition itself. This leads to, two ways of proving a proposition directly or indirectly and the proofs obtained are called direct proof and indirect proof and further each has three different ways of proving which is discussed below. Direct Proof It is the proof of a proposition in which we directly start the proof with what is given in the proposition.

(i) Straight forward approach It is a chain of arguments which leads directly from what is given or assumed, with the help of axioms, definitions or already proved theorems, to what is to be proved using rules of logic.

Consider the following example:

Example 1 Show that if x2 – 5x + 6 = 0, then x = 3 or x = 2.

Solution x2 – 5x + 6 = 0 (given)

Please refer to attached file for NCERT Class 12 Mathematics Proofs In Mathematics

## Tags:

Click for more Mathematics Study Material
 NCERT Class 12 Mathematics Proofs In Mathematics
 NCERT Class 12 Mathematics Mathematical Modeling
 NCERT Class 12 Mathematics Answers and Solutions
 NCERT Class 12 Mathematics Answers and Solutions

## Latest NCERT & CBSE News

Read the latest news and announcements from NCERT and CBSE below. Important updates relating to your studies which will help you to keep yourself updated with latest happenings in school level education. Keep yourself updated with all latest news and also read articles from teachers which will help you to improve your studies, increase motivation level and promote faster learning

### National Youth Day and Birth Anniversary of Swami Vivekananda

Ministry of Education, Govt. of India vide D.O No. 12-4/2021-IS.4 dated 04.01.2022 intimated that 12 January 2022 will be celebrated as “National Youth Day” and “Birth Anniversary of Swami Vivekananda”.   All Schools affiliated to CBSE may celebrate 12 January 2022 as...

### Pariksha Pe Charcha 2022

The 5th edition of Pariskhas Pe Charcha the unique interactive program of Hon’ble Prime Minister with students teaches and parents will be held through virtual mode in February, 2022. In order to select participants who will be featured in Pariksha Pe Charcha programme...

### CBSE Science Challenge 2021 22

Science is inexplicably linked with our lives and helps us to understand the world around us better. Scientific and technological developments contribute to progress and help improve our standards of living. By engaging with this subject, students learn to think, solve...

### Board Exams Date Sheet Class 10 and Class 12

Datesheet for CBSE Board Exams Class 10  (Scroll down for Class 12 Datesheet) Datesheet for CBSE Board Exams Class 12

### All India Children Educational Audio Video Festival

The Central Institute of Educational Technology (CIET), a constituent unit of National Council of Educational Research and Training (NCERT), is inviting entries for the 26th All India Children’s Educational Audio Video Festival (AICEAVF). This festival showcases the...

### Celebration of Matribhasha Diwas Mother Language day

UNESCO has declared 21st February of every year to be celebrated as International Mother Language day to promote dissemination of Mother Language of all, create awareness of linguistic and cultural traditions and diversity across the world and to inspire solidarity...