Mathematical Reasoning Class 11th Notes - Free NCERT Class 11 Maths Chapter 14 notes - Download PDF

# Mathematical Reasoning Class 11th Notes - Free NCERT Class 11 Maths Chapter 14 notes - Download PDF

Edited By Ramraj Saini | Updated on Mar 22, 2022 05:35 PM IST

Notes for Class 11 Maths chapter 14 are regarding mathematical reasoning. In chapter 14 we will be going through the truth values concepts in Mathematical Reasoning Class 11 notes. This Class 11 Maths chapter 14 notes contains the following topics: sentence, compound sentence, connectives like the conjunction, disjunction, implication, biconditional, negation, contrapositive, converse, inverse, validation.

NCERT Class 11 Math chapter 14 notes contain. NCERT Class 11 Math chapter 14 contains a detailed explanation of topics- Simple statements, Compound Statements, Connectives, Negation, Conjunction, Disjunction, Implications, Biconditional, Contrapositive, Converse, Inverse, Quantifiers. NCERT Notes for Class 11 Math chapter 14 is a detailed explanation of the chapter. It also contains FAQ’s that are frequently asked questions by students which can clarify many doubts of them. Every concept that is in CBSE Class 11 Maths chapter 14 notes is explained here in a simple way. All these concepts can be downloaded from Class 11 Maths chapter 14 notes pdf download, Mathematical Reasoning class 11 notes, Class 11 Mathematical Reasoning notes pdf download.

Also, students can refer,

## NCERT CLASS 11 CHAPTER 14 NOTES

A statement is a sentence that can either be true or false but not both at the same time.

Eg: 4 is greater than 10.

Even though it is false as it gives either true or false is a statement.

A sentence cannot be a statement when :

i) if it is an exclamation

Eg: Wow! It is so beautiful. (is not a statement)

ii) if it is a question

Eg: How are you? (is not a statement)

iii) if it is a command or request

Eg: Please get me a glass of water. (is not a statement)

## Simple Statements:

Statements that are not further divided into two or more sentences are called Simple sentences.

## Compound Statements:

Statements that can be further divided into two or more sentences are called Compound sentences.

They are generally joined using “and’, “or”.

Eg: 2 is an even number.

2 is a prime number.

Compound Sentence: 2 is both an even and a prime number.

## Connectives:

1. Negation:

It is basically the opposite of the given statement.

If P is a given statement then the negation of a statement is denoted as ¬P.

Eg: Potatoes are my favorite vegetables. (statement)

Negation: Potatoes are not my favorite vegetables.

TRUTH TABLE:

 P ¬P T F F T
1. Conjunction:

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The statements p and q are joined using “and” form a compound statement then p and q are the conjunctions.

This is denoted using symbol:∧

Eg:

He likes tea.

He likes coffee.

Conjunction:

He likes both tea and coffee.

TRUTH TABLE:

 p q p∧q T T T T F F F T F F F F
1. Disjunction:

The statements p and q are joined using “or” that form a compound statement then p and q are the disjunctions.

This is denoted using symbol: ∨

Eg: He likes tea or he likes coffee.

TRUTH TABLE:

 p q p∨q T T T T F T F T T F F F
1. Implications:

The statements that use “if-then” or “only then” to form compound sentences are called implications.

It is denoted by symbol: → or ⇒

Eg: If you work hard then you can pass the exam.

TRUTH TABLE:

 p q p⇒q T T T T F F F T T F F T
1. Biconditional:

If two sentences are joined using “if and only if”

Then such statements are called biconditional statements.

Denoted using the symbol: ↔ or ⇔

TRUTH TABLE:

 p q p⇔q T T T T F F F T F F F T
1. Contrapositive:

If two statements are reversed and then negated under implication conditions then such statements are contrapositive statements.

TRUTH TABLE:

 p q ¬q⇒¬p T T T T F F F T T F F T
1. Converse:

The reverse of implication statements gives us the converse statements.

TRUTH TABLE:

 p q q⇒p T T T T F T F T F F F T
1. Inverse:

Negation of implication conditions is called inverse statements.

TRUTH TABLE:

 p q ¬p⇒¬q T T T T F T F T F F F T

## Quantifiers:

We have two types of quantifiers.

1. Universal Quantifiers: These quantifiers are those that are suitable for all values.

We use words like “for all” and “for every.”

1. Existential Quantifiers: These are quantifiers that are used or satisfying for only a few particular values.

We use words like “there exists”.

It is denoted by the symbol:∃

## Validity of Statements:

Validity is known from the values if they are true or false.

1. “p and q” are true if we have only both p and q are true.

1. “p or q “ is true when both p and q are true or anyone among p and q is true.

1. “p if q” is true only if p and q both are true or if p is false and q is true or if p and q both are false.

With this topic we conclude NCERT Class 11 chapter 14 notes.

The link for NCERT textbook pdf is given below:

URL: ncert.nic.in/textbook/pdf/kemh114.pd

## Significance of NCERT Class 11 Maths Chapter 14 Notes:

NCERT Class 11 Maths chapter 14 notes will be very much helpful for students to score maximum marks in their 11 board exams. In Mathematical reasoning Class 11 chapter 14 notes we have discussed many topics: sentence, compound sentence, connectives like: conjunction, disjunction, implication, biconditional, negation, contrapositive, converse, inverse, validation, and truth tables. NCERT Class 11 Maths chapter 14 is also very useful to cover major topics of Class 11 CBSE Maths Syllabus.

The CBSE Class 11 Maths chapter 14 will help to understand the chapter in details. Students can get the document from Mathematical Reasoning class11 chapter 14 pdf download.

## NCERT Class 11 Notes Chapter Wise.

 NCERT Class 11 Maths Chapter 1 Notes NCERT Class 11 Maths Chapter 2 Notes NCERT Class 11 Maths Chapter 3 Notes NCERT Class 11 Maths Chapter 4 Notes NCERT Class 11 Maths Chapter 5 Notes NCERT Class 11 Maths Chapter 6 Notes NCERT Class 11 Maths Chapter 7 Notes NCERT Class 11 Maths Chapter 8 Notes NCERT Class 11 Maths Chapter 9 Notes NCERT Class 11 Maths Chapter 10 Notes NCERT Class 11 Maths Chapter 11 Notes NCERT Class 11 Maths Chapter 12 Notes NCERT Class 11 Maths Chapter 13 Notes NCERT Class 11 Maths Chapter 14 Notes NCERT Class 11 Maths Chapter 15 Notes NCERT Class 11 Maths Chapter 16 Notes

### NCERT Books and Syllabus

 NCERT Book for Class 11 NCERT Syllabus for Class 11

1. When can we say that it is a statement in Mathematical Reasoning Class 11 notes ?

It is said to be a statement if it is a fact or if it answers it to be either true or false.

2. Who invented Class 11 Math chapter 14 notes?

Ancient mathematicians, mostly the Greeks, invented mathematical reasoning.

3. Name the responsive skills in NCERT notes for Class 11 Math chapter 14 ?

We have five responsive skills. Namely they are:

induction, deduction, inference, analysis, and evaluation.

4. What is the use of Mathematical Reasoning Class 11 notes in real life?

It is basically very useful to analyse a real life situation based on mathematical reasoning concepts.

5. Can you give an example of a Biconditional statement according to Mathematical Reasoning Class 11 notes?

“A polygon is said to be a triangle if and only if it has three sides “

is an example for biconditional statements.

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