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An Italian student, a young man of twenty, came to me today with a bunch of papers in his bag. It was the questions and answers to a multiple choice English quiz. We're talking hundreds of questions. He needs to pass this exam really well if he has any hope of being accepted in a military academy.

We go through the questions and answers that he is unsure of until we reach this one…

Choose the alternative which is closest in meaning to the word in brackets and which does not change the meaning of the sentence. “The question is [irrelevant]”

[ ] not respectful

[ ] hard to answer

[ ] inappropriate

[ ] very important

[x] everywhere and nowhere

He reasoned that "inappropriate" was the best choice but the so-called correct answer is the one marked x. I don't think neither is right and the "correct" answer is an idiom with which I am very unfamiliar. The expression that I do know is “neither here nor there”

Wiktionary defines it

Having no significance or influence on the question at hand.

The synonyms listed are: beside the point, betwixt and between, irrelevant, unimportant, unrelated, impertinent

But it has been many years since I lived in the UK, and maybe “everywhere and nowhere" is used nowadays. Google tells me it is the title of an English 2011 film, which suggests that the idiom(?) is used but it is not listed in any of the main dictionaries I consulted.

Oxford Dictionaries
Collins Dictionary
Merriam-Webster
WordNet

1. Is the answer “everywhere and nowhere” in the multiple choice quiz right or wrong? Please provide supporting evidence.

I would have also picked everywhere and nowhere if forced to choose between those options. But I wouldn't have been happy about it.

Without actually looking at a thesaurus, when I hear the word irrelevant I think to myself immaterial, unrelated, not useful, beside the point, off topic, and has no bearing. Only one of those is what Wiktionary lists. Further, I would never associate irrelevant with impertient—so I find that synonym strange. (But that's just based on my personal associations.)

By the process of elimination, I immediately ruled out the first four possible answers. (Unlike the Italian student, I would never associate irrelevant with inappropriate. That word has a negative connotation to it that I don't get from irrelevant.)

That left me only with everywhere and nowhere.

When I hear everywhere and nowhere, I think to myself unhelpful and meaningless. Those are at least close to irrelevant—and certainly closer, in my mind, than any of the other options.

But, as I say, it's more a process of elimination for me than an affirmative statement. (A kind of two-step equivalence.) Everywhere and nowhere is certainly not something that would leap into my mind as meaning irrelevant.

Having now composed my answer (not having wanted to have research affect my subjective response), I see that Merriam-Webster shows the following in its thesaurus for irrelevant:

Phrases Synonymous with IRRELEVANT

beside the point, neither here nor there

I note that neither here nor there has almost the same meaning (or non-meaning) as everywhere and nowhere.