PREDICATE LOGIC and QUANTIFIER NEGATION - DISCRETE MATHEMATICS

Today we wrap up our discussion of logic by introduction quantificational logic. This includes talking about existence and universality. We also discuss the negation of our quantificational operators.
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[@klevisimeri607]

More easy way to derive the formulas:
For quantifiers:
¬∀x ∃x 1.
Multiplying with "not" both ways (like multiplying with minus both ways): ¬¬∀x ¬∃x
∀x ¬∃x 2.
For function just multiply the not:
¬(P(x)) ¬P(x)
So for example:
∀x P(x)
Do distribution of not:
¬(∀x P(x))
Like multiplying (with not in out case):
¬∀x ¬P(x)
Using 1. :
∃x ¬P(x)

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[@dtirey]

Very helpful, but have one question. On the last problem, why didn't the quantifiers flipped and negated like the four practice problems before? Thanks

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In a situation where you would have a double negation through the simplification of a problem similar to the last one you've done, does that double negation law applies to quantifiers/predicates as well or is that to be treated some other way? Thank you!

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So if I try to put in a sentence what you did at the end of the video after doing the negation, can I say it as 'is there an x for all y such that not P( x, y ) or not Q( y )

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