"The larger of A and B" or "the larger of A or B"

I was wondering which one is more correct between "the larger of A and B" and "the larger of A or B".

I use the former, but I saw in IRS instruction for Form 1040:

In most cases, your federal income tax will be less if you take the larger of your itemized deductions or standard deduction.

Ask a computer programmer if they want tea or coffee and they will say yes!

Ask them if they know people born in New York and Washington they will say no (you can't be born in NY AND Washington)

It's probably a bad idea to take grammar advice from someone who would answer "Yes" to the question "Do you want tea or coffee?" :-) This sort of thing is just an exercise in interpreting natural language as strict propositional logic, which can be a fun past-time for some species of nerds, but isn't really relevant to the question at hand, which is about correct usage.

@Marcin above, I think, has it basically right: either is probably fine.

Personally I agree with you and use the "and" construction. To me, it feels as if the "and" is being used to describe a set of things, and then the "larger" is like a function that applies to that set.

So I'd say: "The larger of the two" "The larger of A and B" "The largest of A, B, C and D" "The largest of the Beatles"

What's nice here is that you preserve substitutability amongst the different ways of describing the set, i.e.: "A and B are the two" "A, B, C, and D are the Beatles"

Notice that if you use the "or" construction, this doesn't work out: "The larger of the two" "The larger of A or B" "The largest of A, B, C, or D" "The largest of the Beatles "A or B are the two" //wrong! "A, B, C, or D are the Beatles" //wrong!

But of course ultimately what trumps everything is what sounds right to and is used by English speakers, and as @Macin says both ways seem to be ok. But to me this sort of reasoning can break the tie. :-)

The larger of A or B = The larger of (A or B) -> True because one of them has to be true. Thus, the former expression is proper.

Note: I am a computer scientist :)

Either is probably fine - it seems that "and" and "or" are both sometimes use disjunctively. This has lead to substantial litigation where it is not clear whether "and" is being used disjunctively or conjunctively.