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

Updated on 22 Mar 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.

This Story also Contains

NCERT CLASS 11 CHAPTER 14 NOTES
Simple Statements:
Compound Statements:
Connectives:
Quantifiers:
Validity of Statements:
Significance of NCERT Class 11 Maths Chapter 14 Notes:
NCERT Class 11 Notes Chapter Wise.

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:

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

Conjunction:

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

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

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

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

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

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

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.

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

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

$\text { It is denoted using the symbol: }\forall$

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.

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

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

“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

Subject Wise NCERT Exemplar Solutions

Subject Wise NCERT Solutions

NCERT Books and Syllabus

NCERT Book for Class 11

NCERT Syllabus for Class 11

Articles

IOQM Admit Card 2025: Download Indian Olympiad Qualifier in Mathematics Hall Ticket

Aug 29, 2025

Cambridge IGCSE Result 2025: Check Cambridge IGCSE Result Dates & Grading System

Aug 26, 2025

Anuprati Coaching Yojana 2025-26 : Scheme Dates, How to Apply, Benefits, Selection Process

Aug 26, 2025

Anuprati Coaching Yojana Eligibility Criteria 2025-26 : Categories: SC, ST, OBC, MBC, and EWS

Aug 26, 2025

Popular Questions

A block of mass 0.50 kg is moving with a speed of 2.00 ms^-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

Read Complete Answer

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up ? Fat supplies 3.8×10⁷J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 ms⁻² :

Option 1)

2.45×10⁻³ kg

Option 2)

6.45×10⁻³ kg

Option 3)

9.89×10⁻³ kg

Option 4)

12.89×10⁻³ kg

Read Complete Answer

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

Read Complete Answer

A particle is projected at 60⁰ to the horizontal with a kinetic energy $K$ . The kinetic energy at the highest point

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

Read Complete Answer

In the reaction,

$2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

Read Complete Answer

How many moles of magnesium phosphate, $Mg_{3}(PO_{4})_{2}$ will contain 0.25 mole of oxygen atoms?

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

Read Complete Answer

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

Read Complete Answer

With increase of temperature, which of these changes?

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Read Complete Answer

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol^-1) is

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

Read Complete Answer

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t²) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m² , the number of rotations made by the pulley before its direction of motion if reversed, is