Basics of Mathematical reasoning

Basic terminology of Mathematical Reasoning

The sentences which are true or false but not both are called statements or mathematically acceptable statements. 

The sentences which contains variable time, variable distances are not considered as statements.

A sentence which is an exclamation, wish, imperative or interogative can't be a statement. 

The statement which is true and false is represented by 'T' and 'F'. 

Simple statement

The statement whose true value is not depend on other statement is called simple statement. 

Compound statement

The statement which is combination of two or more simple statements are called compound statements. 

Here, the simple statement which form compound statement are known as component statements. 

Connectives

AND (conjunction) 

The connective 'and' will be true if both of its component statements are true. 

OR (disjunction)

The connective 'OR' will be true when any one of the component statement is true. 

Inclusive OR

When both the component statements can hold simultaneously. 

Exclusive OR

When both the component cannot hold simultaneously. 

If...then (conditional)

If and only If (Bi-conditional)

p<->q = (p→q)^(p→q) 

          = (~pvq)^(~qvp)

Negation

Tautology

The statement which is always true is represented by 't'. 

Contradiction/Fallacy 

The statement which is always false. It is represented by 'f'. 

Converse 

The converse of the statement (p→q) is (q→p)

Inverse

The inverse of the statement p→q is ~p→~q

Contrapositive

A contrapositive statement of p→q is 

~q→~p 

*For high school studies