washthe car evenif the weatherisnotnice.
Converse,Inverse,and Contrapositiveof an If-ThenStatement
Lookat statement1 aboveagain.
If the weatheris nice,then I’ll washthe car.This can be representedin a diagramas:
If then.= the weatheris nice = I’ll washthe car“If then ” is also writtenas
Noticethat conditionalstatements,hypotheses,and conclusionsmay be true or false. and the statement
“If then may be true or false.
In deductivereasoningwe sometimesstudystatementsrelatedto a givenif-thenstatement.Theseare
formedby using and their opposites,ornegations(“not”).Notethat “not ” is writtenin symbolsas
.and can be combinedto producenew if-thenstatements.- Theconverseof is
- Theinverseof is
- Thecontrapositiveof is
Now let’s go backto statement1: If the weatheris nice,then I’ll washthe car.
= the weatheris nice
= I’ll washthe car
= the weatheris not nice= I’ll washthe car (or I washthe car)
= I won’twashthe car (or I don’twashthe car)Converse: If I washthe car, then the weatherwas nice.
Inverse: If the weatheris not nice,then I won’twashthe car.
Contrapositive: If I don’twashthe car, then the weatheris not nice.Noticethat if we acceptstatement1 as true, then the converseand inversemay, or may not, be true. But
the contrapositiveis true. Anotherway to say this is:The contrapositiveis logicallyequivalentto the original
if-thenstatement. In futureworkyou may be askedto provean if-thenstatement.If it’s easierto provethe