# “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.

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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)

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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. :-)

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It's pastime, coming from 'pass time'. And 'A is the larger of the two or B is the larger' is correct both logically and grammatically; you couldn't rewrite it using 'and'. But nitpicks aside, good answer. – TimLymington Jun 29 '11 at 11:54
natural language should be interpreted as strict propositional logic. – chiliNUT Mar 6 '14 at 7:32

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 :)

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+1 for a great answer :) computer programmer here too ! :) – RiMMER Apr 18 '11 at 22:44

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.

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There's a subtle mathematical difference between the two ways of saying it. In the "or" case you're giving a list of the items that must be selected among. In the "and" case you're defining a set of items and asking about one of them.

The "or" makes me think that the "larger" applies to the items listed. "Which would you like, coffee or tea or me?"

The "and" makes me think of the items listed as elements of a set. For example, "Which of our delicious drinks would you like?" "Well, what is your list of drinks?" "We have coffee and tea and water."

I would generally use the "or". But if I wanted to stress the incorporation of the list of items into a set, rather than the modifier "larger", the "and" might be better.

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Sorry Mr/Ms Computer Scientist ... It may be "true" for binary systems but it's not comprehensible linguistically. If you say "The larger of A or B" or "The larger of (A or B)" you have only said "The larger of A or the larger of B", which is nonsensical. The only way to make this sensible is to indicate that "the larger of" means the larger of BOTH THINGS TAKEN TOGETHER (i.e., A and B). Neither A nor B can be "larger" except in relation to the other. If you do not group the two things together (by using "and") you have no set within which to make a comparison, so you can't determine which of them is "the larger" (i.e., the larger compared to what?) You are relying on your parentheses to group them together, but this doesn't avoid the need to connect A and B with "and" within those parentheses. (Note: I am a legislative drafter.)

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