Conditional Statements

Front

What is a conditional statement?

Back

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."

Front

What is the inverse of a conditional statement?

Back

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

Front

What is the converse of a conditional statement?

Back

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

Front

What is the contrapositive of a conditional statement?

Back

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

Front

What is a biconditional statement?

Back

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

Front

Identify the inverse: If it rains, then the ground is wet.

Back

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

Front

Identify the converse: If it rains, then the ground is wet.

Back

If the ground is wet, then it rains.

Front

Identify the contrapositive: If it rains, then the ground is wet.

Back

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

Front

What is the relationship between a statement and its contrapositive?

Back

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

Front

What is the relationship between a statement and its converse?

Back

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