CK-12 Geometry-Concepts

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

2.3 Converse, Inverse, and Contrapositive

Here you’ll learn how to find the converse, inverse and contrapositive of a conditional statement. You will also learn
how to determine whether or not a statement is biconditional.

What if your sister told you "if you do the dishes, then I will help you with your homework"? What’s a statement that
is logically equivalent to what your sister said? After completing this Concept, you will know how to answer this
question as you discover converses, inverses, and contrapositives, and how changing a conditional statement affects
truth value.

Watch This

MEDIA

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CK-12 Foundation: Chapter2ConverseInverseContrapositiveA

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James Sousa: Converse, Contrapositive, and Inverse of an If-Then Statement

Guidance

Consider the statement:If the weather is nice, then I will wash the car.This can be rewritten using letters to represent
the hypothesis and conclusion:

Ifp,thenq where p=the weather is nice and q=I will wash the car. Or,p→q.

In addition to these positives, we can also write the negations, or “not”s ofpandq. The symbolic version of notp,
is∼p.

∼p=the weather is not nice ∼q=I will not wash the car

Using these negations and switching the order ofpandq, we can create three more conditional statements.