Logic 101 (#19): DeMorgan's Law, Part 1

Fun fact: p ^ q is the same thing as ~(~p v ~q).

The rule is named after Augustus De Morgan, a 19th Century British mathematician. Some refer to it as a "rule," others a "law," and yet others a "theorem." It's the same thing in each case.

[mistemail]

Why does everything else say there’s a negation on both sides? Isn’t it supposed to be:
~(p&q) is the same as ~p v ~q
and
~(pvq) is the same as ~p & ~q
?

[justinhansen]

Thanks for the explanation. The idea that statements have certain conditions and that we flip all the possible conditions with a negation makes so much sense and helped me understand what's going on.

[Shapeplusform]

You got me with the ~ ( ~ P v ~ Q )
I rushed it and guessed P v Q

[melvinvasquez]

Thanks!!! Finally a video that flat out tells you WHY this would be useful; instead of just proving that the law works out thru a truth table. Hot dam I am glad someone gets it! Sometimes the answer us noobs are looking for isn't so obvious lol.

[xfa_]

Is there a possibility to apply logic in natural conversations between two persons? I mean if it is possible for the logic to be applied on simple sentences, is it possible as well to apply this in conversational statements?
Thanks

[crash]

=) thanks for making the videos my lecturer didnt explain this very well but your videos make it easy to understand :) so now ill be able to get my degree

[Marta_mt]

I don't understand why a negative v (or) becomes ''and''. Did I miss something?

[gidrengidrenovi]

How do you write ~(~P v ~Q) into natural english so that brackets would apply? Whether I am not dancing or I am not listening to african beats, it is not the case. Am I missing something?

[TheMorhaGroup]

If "and" is the negated product of "or". What then is "and"s negated product? It can't be "or", as the opposite of both occurring is neither occurring, not either, or booth. It would be exclusively non.
The opposite of "you and John can come" cannot be "the either, neither, or both of you can come"
🤔

Edit:
"negations flip the truth values" is an interesting statement to make, after calming that the negation function can also flip a non-truth value, into another, non-truth value

[StevieBaskin]

I think you're staying things incorrectly at 1:58

~(could be ~P)
You said "It can't be the case that it could be P"
You should have said "it can't be the case that I could be not-P)

[TlogicoP]

~(~Pv~Q) and P^Q are NOT 'the same thing'. They are logically equivalent.

[PunmasterSTP]

Anyone else think of The Captain, or is it just me?

[milethebestmb]

To put it into real life:
P is ice cream
Q is chocolate
You shouldn't buy chocolate or ice cream
which is P' v Q'
so it says you can buy chocolate or ice cream or neither. And if we negate it, there is one thing left: you should buy ice cream and chocolate (which is p^q)