My apples and orange are wrong
My apples and orange is wrong
I am not a native English speaker, and I am having some trouble choosing between plural are or singular is for that kind of example.
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It's hard to conceive of a situation in which apples and oranges could be wrong, but let's suppose there is.
Assuming you really mean apples (plural) and orange (singular), the first construction is correct.
My apples and orange are wrong.
You are speaking of multiple things, and even if both were singular
My apple and orange are wrong.
the copula (verb of being) would still be plural.
In most cases this comparison is done in the plural on bother sides of the equation.
Compare apples and oranges.
This comparison is generally understood to mean that the comparison is unfair, as the two objects being compared are not similar enough.
A nice variation on this theme, that I have heard being used to accentuate the fact that dissimilar objects are being compared is:
Your comparison is invalid, you might as well be comparing apples with pigs
Conjunctions with conflicting case agreement are tricky, and relatively rare in written English. Johannssen (1998) in her book dedicated to this particular problem in English and Spanish gives a strong argument that when the conjuncts differ, the first (in Head-first languages) usually has agreement wit the rest of the sentence, while the others tend to some neutral or uninflected default for the language. Under her theory, which is the most comprehensive that I have found, because 'apples' is the first conjunct in your example sentence, you should use 'are', but if 'orange' is first, you should use 'is'. My personal preference would be to raise the conjunction to avoid this issue. For example:
My apples are wrong, and so is my orange.