“Inclusive or” doesn’t specifically mean “saying yes when someone asks an X or Y question”.

Inclusive or is the general function that takes X and Y as inputs and returns true if either one of of X or Y is true. Which is in contrast to an exclusive or, which returns true if exactly one of X or Y is true, but not both. So the joke is “you expected this to be an exclusive choice between two options, but I interpreted it as an inclusive or and said yes, indicating that one or the other is true but without telling you which one”.

If the answer is “no” to an inclusive or, then neither X nor Y is true: which cashes out to normality. Like “Do you want tea or coffee? – No” means you want neither tea nor coffee. Whereas if the answer is “no” to an exclusive or, then it could be the same case where neither X nor Y is true, but it could also be because they’re both true. So “Do you want tea xor coffee – No” would be ambiguous between “I don’t want either” and “I want tea AND coffee”.

Still an inclusive or

https://en.wikipedia.org/wiki/Logic_gate

I’m pretty sure it’s just plain “nor” but I don’t know, I ain’t no logician.

That would be a “NAND” Gate as far as I know.

You mean like this? https://en.wikipedia.org/wiki/XNOR_gate

You need more info and the whole truth table. There’s a few functions of f(x,y) that would yield true when both x and y inputs are true. In general though, exclusive or (XOR) is common-use English “or”. Inclusive or (OR) is what you mention, and then the inverse of OR is NOR which may be what you are talking about or the inverse of XOR or XNOR or NORX depending on the textbook.

This is all digital logic stuff, and I’m not sure if logic involves in philosophy would use the same naming.

Exclusive and