Conditional Statements

A conditional statement is a logical statement that has two parts: a hypothesis (if part) and a conclusion (then part). It is often written in the form "If P, then Q."

The inverse of a conditional statement "If P, then Q" is "If not P, then not Q."

The converse of a conditional statement "If P, then Q" is "If Q, then P."

The contrapositive of a conditional statement "If P, then Q" is "If not Q, then not P."

A biconditional statement is a statement that combines a conditional statement and its converse, written as "P if and only if Q."

If it does not rain, then the ground is not wet.

If the ground is wet, then it rains.

If the ground is not wet, then it does not rain.

A statement and its contrapositive are logically equivalent; they have the same truth value.

A statement and its converse are not necessarily logically equivalent; they can have different truth values.