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https://www.youtube.com/watch?v=xXaFCq0eesc Ever wonder what happens if something is both true and false, that is $Pwedge neg P$? For mathematicians, it is a doomsday scenario because it causes everything else to be both true and false as well. This is called the principle of explosion.

https://www.youtube.com/watch?v=PR0bBAZUlG4 We discuss why the classic logical arguments of modus ponens $$P,Prightarrow Q, Q$$ and modus tollens $$neg Q, Prightarrow Q,neg P$$ are valid forms of argument.