## Chapter 14

## Mathematical Reasoning

A sentence is called mathematically acceptable statement if it is either true or false not both

**Statements:**

Two plus two equals four

8 is less than six

The sum of all interior angles of a triangle is 1800

The product of -1 and 8 is 8

Not a statement:

Mathematics is difficult

The sides of a quadrilateral have equal length

Answer this question

Today is a windy day

He is a mathematics graduate

Kashmir is far from here

Open the door

While dealing with statements,we usually denote them by small letters p,q,r…

P: fire is always hot

Q: All real numbers are complex numbers

Negation of a statement

The denial of a statement is called its nagation

Chennai is a city

Chennai is not a city

It is false that Chennai is a city

It is not the case that Chennai is a city

The negation of p is denoted by

Q. Every natural number is an integer

~p : It is false that every natural number is an integer

Compound statements

A statement obtained by combining two or more statements using connecting words like “0r”, “and” etc. are called compound statements. Each statement is called component statement

Q. The sky is blue and the grass is green

Component statements are:

The sky is blue

The grass is green

Q. All integers are positive or negative

Component statements are:

All integers are positive

All integers are negative

A compound statement with “And ” is true if all its component statements are true

A compound statement with “Or ” is true if at least one of its component statement is true

Inclusive”Or”, exclusive”Or”

To enter a country, you need a passport or voter registration card

Inclusive”Or”

Two lines intersect at a point or they are parallel

exclusive”Or”

The school is closed if it is a holiday or a Sunday

Inclusive”Or”

Students can take Hindi or Malayalam as second language

exclusive”Or”

Quantifiers

The phrases like “There exists”, ”For every”, ”For all” are called quantifiers

Identify the quantifier

Q. There exist a number which is equal to its square

There exist

Q. There exist a capital for every state in India

There exist, for every

Statement with “if-then”

If a number is a multiple of 9 then it is a multiple of 3

P: a number is a multiple of 9

q: a number is a multiple of 3

if p then q

Stay tuned

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