CK-12 Geometry Concepts

http://www.ck12.org Chapter 2. Reasoning and Proof

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

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CK-12 Foundation: Chapter2ConverseInverseContrapositiveA

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James Sousa:Converse, Contrapositive, and Inverse of anIf-ThenStatement

Guidance

Consider the statement: If the weather is nice, then I will wash the car.

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.