# Videos

## 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.