2018-12-23

Propositional logic: Contrapositive

Just a quick note about the contrapositive is that it’s very useful to prove some statement. For example:

All drivers in Madrid, drive a bike
— original statement
50c8bc1a5046d2c61e4af316a3ce3777.png

Now if we can prove that the contrapositive is true, then we can prove that the original statement was wrong.

All non-bike drivers, live outside Madrid
— contrapositive
16198337375010f3fd72425bf893ce04.png

Only proving that at leat one non-bike driver lives in Madrid will prove the initial statement to be wrong.