Inverse Converse and Contrapositive

Front

What is a conditional statement?

Back

A conditional statement is an if-then statement that expresses a relationship between two propositions, where one proposition (the hypothesis) implies the other (the conclusion).

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

Identify the hypothesis in the statement: 'If it rains, then the ground is wet.'

Back

The hypothesis is 'It rains.'

Front

Identify the conclusion in the statement: 'If it rains, then the ground is wet.'

Back

The conclusion is 'The ground is wet.'

Front

What is the relationship between a statement and its contrapositive?

Back

A statement and its contrapositive are logically equivalent; if one is true, the other is also true.

Front

What is the relationship between a statement and its inverse?

Back

A statement and its inverse are not logically equivalent; one can be true while the other is false.

Front

What is the relationship between a statement and its converse?

Back

A statement and its converse are not logically equivalent; one can be true while the other is false.

Front

Provide an example of a conditional statement.

Back

If a shape is a square, then it has four equal sides.