CK-12-Pre-Calculus Concepts

16.4. Inverse, Converse, and Contrapositive http://www.ck12.org

16.4 Inverse, Converse, and Contrapositive

Here you will examine the implications of the inverse, converse and contrapositive statements as they relate to a
conditional statement.
The typical conditional statement isP→Q. The inverse, converse and contrapositive are each related to the
conditional statement but are not always identical. Which type of statement is always equivalent to the original?

Watch This

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/63160

http://www.youtube.com/watch?v=IHd8jiUF3Lk James Sousa: The Converse, Contrapositive, and Inverse of an
If-Then Statement

Guidance

Consider a conditional statementP→Qwhere:

• P=It is raining.


• Q=T he driveway is wet.

Original Conditional:P→Q= If it is raining, then the driveway is wet.

TABLE16.14:

P Q P→Q

T T T

T F F

F T T

F F T

The inverse of a conditional negates both the hypothesis and the conclusion.
Inverse:∼P→∼Q= If it is not raining, then the driveway is not wet.

TABLE16.15:

P Q ∼P ∼Q ∼P→∼Q

T T F F T

T F F T T