Conditional Statements

A conditional statement(p→q) where one idea is based on another. It is written in if-then format. 

Example: If it is snowing, then it is cold outside.

The converse(q→p) of a conditional statement is the opposite or reverse. 

Example:  If it is cold outside, then it is snowing. 

This statement does not make sense as it could be cold outside without snow, meaning the converse does not make sense. 

The inverse ( ~p → ~q) is the negation of a conditional statement. 

Example: If it is not snowing outside, then it is not cold. 

This statement does not make sense as it can be cold outside when snow is inexistent. 

The contrapositive( ~q→~p)of a statement is the inverse and converse combined. It involves the reverse and negation of the conditional statement. 

Example: If  it is not cold outside, then it is not snowing. 

This sentence does make sense. 

Generally, the contrapositive and conditional statement are true while the inverse and converse are false. 

A biconditional statement is true both ways. Usually contains “if and only if”.

Example: I will go to the movies if and only if it stops raining.