Following Along Async Tutoring [Dface]

[Dface]

@Elliot

@Eternity

@Elliot

Yes. So what small set of operators have you discovered is universal?

Also what universal sets can you make from: {and, or, not}?

I’m kind of confused what you’re asking here. The confusion is about “what universal sets can you make” and “what small set of set of operators have you discovered is universal”. Aren’t those the same thing?

The first one asks for any set. The second one asks for a subset of {and, or, not}.

I think you can make and, or, not with nand. Here are my truth tables:
Truth table for and(x,y) = nand(nand(x,y),nand(x,y)):

Truth table for not(x) = nand(x,x):

Truth table for or(x,y) = nand(nand(x,x), nand(y,y))

nand(nand(x,y),nand(x,y))

I remember before that ET said {and, or, not} are a universal set of logic operators:

@Elliot

It turns out that {and, or, not} is a universal set of logic operators (this is closely related to stuff you may have heard about computational universality). You can construct all the other operators from them.

If nand can make not, and, or and not, and, or can make all other logic operators, that means nand can also make all other operators. I bet nor can make all other operators too.

To answer the first question I think a small set of universal logic operators is {nand}. Idk if “operators” in the first question means that I have to include two operators.

For the second question, I had to look up what a subset is. I think you can make the universal sets {and, not} or {or, not} from {and, not, or}.

I read ahead and found this question:

@Elliot

@Eternity

@Elliot

Yes. So what small set of operators have you discovered is universal?

{nand, nor}

If you use only one of those, what can and can’t you make from the set {and, or, not}? Or put another way, what is each adding that the other is missing?

nand isn’t missing anything as a universal set cuz it can make nor too.

I read ahead and ET asked @Eternity a question:

@Elliot

So what’s a smaller universal set than {nand, nor}?

@Eternity’s answer:

@Eternity

{nand} or {nor}

ET’s response:

@Elliot

Yeah. Lots of small sets are universal.

Ok cooll you can make a universal set with just nand or just nor