Page 1 - LESSON NOTE

CHAPTER-14 MATHEMATICAL REASONING

LESSON NOTES

Statement
A sentence is called a mathematically acceptable statement if it is either true or false .

Example:

o Two plus two equals five. FALSE - Statement
o The sum of two positive numbers is positive. TRUE : Statement
o Girls are smarter than boys. Debatable: Not a statement
o Mathematics is fun. Debatable: Not a statement
o Exam Fear is a good educational website. Debatable: Not a statement

NEGATION OF A STATEMENT:
The denial of a statement is called the negation of the statement. It is false that XXXX.

Statement: Three plus two is five
Negation : <It is false that Three plus two is five >
Three plus Two is not five

Statement: Everyone in India peaks Hindi
Negation: < It is false that Everyone in India peaks Hindi >
Not Everyone in India speaks Hindi

Statement: India is a democratic country
Negation : <It is false that India is a democratic country>
India is not a democratic country

Property of Negation of Statement: If p is a statement, then the negation of p is also a
statement and is denoted by ∼ p

Compound & Component Statement
A Compound Statement is a statement which is made up of two or more statements.

Each statement is called a component statement.

Component statement: 7 is an odd number.
Component statement: 7 is a prime number.
Compound Statement: 7 is both odd and prime number.

Connectives: And
The compound statement with ‘And’ is true if all its component statements are true.The
component statement with ‘And’ is false if any of its component statements is false (this