Inverse, Converse, Contrapositive

A conditional statement is a statement that is written in the if-then form.

The part that follows the if is your hypothesis.

The part that follows the then is your conclusion.

Ex.

If it is dark outside, then it is night.

The converse of a conditional if-then statement exchanges the hypothesis and the conclusion.

Ex.

If-then statement: If it is dark outside, then it is night.

Converse: If it is night, then it is dark outside.

The inverse of a conditional if-then statement is the negation of the hypothesis and conclusion of a conditional statement.

To negate a statement, is to give the opposite of the original statement.

Original statement: If you are a guitar player, then you are a musician.

Inverse statement: If you are not a guitar player, then you are not a musician.

The contrapositive of a conditional if-then statement is negating and reversing the hypothesis and conclusion of a conditional statement.

Ex.

Original Statement: If you are a guitar player, then you are a musician.

Contrapositive: If you are not a musician, then you are not a guitar player.