Definitely a repost, but it fits the season
Can I have everything? Inside and outside the Venn circles!
That would be the symbol\operation called TRUE or TOP or “tautology” which is always true. They’re actually missing quite a few of the weirder ops, including implication and
biconditional\iff\if-and-only-if. (Edit: Actually I think XNOR is also the biconditional. I guess pretend like I said “material implication” and “reverse implication”. Fricken booleans man!)
This cheat sheet needs a cheat sheet. What do the numbers with 3 numbers mean?
I truly have no idea and wish I did, haha. It looks like a shorthand for which operation is being followed, maybe like a group theory thing, but I really don’t know.
I never got why “implies” is called that. How does the phrase “A implies B” relate to the output’s truth table?
I have my own “head canon” to remember it but I’ll share it later, want to hear someone else’s first.
“A implies B” means if A is true then B must be true; if A is false, then B can be anything. In other words, the only state not allowed is A being true and B being false. Therefore, the only “hole” is the part of A that doesn’t include B.
Yeah, that one’s always bothered me too. I think the difference in meaning from colloquial “implication” and logical “material implication” are also involved in the raven paradox.
So the statement that “all ravens are black” can be taken as “if RAVEN then BLACK”. Is this statement true? If you see a black raven then trivially yes, if you see a white raven then trivially false (via counter example).
However if you see a non-raven, it is evidence for the truth of the statement because it doesn’t go against it: not-ravens being black-or-not-black both reduce the universe of possible objects without proving not-black-ravens exist.
Or something like that, I think it’s stupid too. Trinary logic can adopt a more sensible (IMHO) definition of implication that makes A being false always lead to the third value (usually defined as indeterminate or neither-true-nor-false).
“A → B” is true in any variable assignment where B is true if A is true.
It has always been mostly obvious to me.
Yeah, that kinda works but I don’t like it. See my reply to the other comment.
Honestly, this meme just legit helped me understand some of the tools in my CAD software.
…goddamn programmers…
my logic is too weak to be able to make sense why those are they way they are, I just brute force each of them until I found which one I need when working with that in Blender shader nodes.
Or it’s closer to Trick XOR Treat or, if we are realistic, Trick NAND Treat
XNOR is so ambiguously named.
Every time, I’m like: The inverse of XOR? Or the inverse of NOR? Oh, right, NOR is already the inverse of OR, so X-NOR is just OR, so XNOR must be the inverse of XOR.
It’s NOR, but the blank spots (because "N"OR) are exclusive - the blank spots can’t overlap.
Gonna save this A very good visual representation
