Inverse, Converse, and Contrapositive

Front

What is the definition of a conditional statement?

Back

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

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 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 contrapositive of a conditional statement?

Back

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

Front

Given the statement 'If I have a Siberian Husky, then I have a dog,' what is the converse?

Back

If I have a dog, then I have a Siberian Husky.

Front

Given the statement 'If angles are congruent, then the measures of the angles are equal,' what is the converse?

Back

If the measures of the angles are equal, then the angles are congruent.

Front

What is the conclusion of the statement 'If angles are congruent, then the measures of the angles are equal'?

Back

The measures of the angles are equal.

Front

What is the difference between a converse and an inverse?

Back

The converse switches the hypothesis and conclusion, while the inverse negates both the hypothesis and conclusion.

Front

How do you form the contrapositive of a statement?

Back

To form the contrapositive, negate both the hypothesis and conclusion of the original statement and switch their places.

Front

If the statement is 'If it rains, then the ground is wet,' what is the contrapositive?

Back

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