Bounded Quantifiers in Logic

https://www.youtube.com/watch?v=LJjJbljEOVs Logical quantifiers are often bounded like $forall xin S: P(x)$. That is, we say that universally or existentially quantified elements satisfy a predicate (like being a member of some set) before stating the condition to be fulfilled. We describe such logical sentences here.

De Morgan’s Laws in Logic

https://www.youtube.com/watch?v=DOu1kjAXutU Learn to negate logical expressions involving disjunctions and conjunctions using De Morgan’s laws $$neg(pvee q) equiv neg p wedge neg q,$$ and $$neg(pwedge q) equiv neg p vee neg q.$$

The Principle of Explosion in Logic

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.

Why Modus Ponens and Modus Tollens are Valid

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.