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
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