Hard Tweets Explained: Contraposition


alfageeek

Contraposition is a logic term that I’m guessing most people don’t know. Here is a simple example.

Me: Did you brush your teeth?

7: Yes!

Me: (checks toothbrush, it is dry)

7: Oh! You mean today?

We start with a conditional implication that if she brushed her teeth, then the toothbrush would be wet.

Brushed —implies—> Wet

We don’t know whether she brushed her teeth, but we do know that the toothbrush is not wet. The logical principle of contraposition (also called modus ponens) says that if you are certain that P->Q, then you can be certain that (not Q)->(not P). If brushed implies wet, then not-wet implies not-brushed.

Note that wet does not imply brushed. Now that 7 is 8…

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