slang - The math problem is too difficult for `X` to work out


There are four options: everybody, somebody, anybody and nobody. Which one should be used in X place ?



Answer



As FF has pointed out, only everybody and anybody are acceptable
(everyone and anyone also work). They work, and the others don't, for the same reasons:




  1. Too is a Negative -- too Adj to VP means 'so Adj that Not VP';
    therefore NPIs like anyone work within its scope,
    and so anybody is used here, instead of somebody.


    That's also why nobody is ungrammatical here, because that would mean
    *The math problem is so difficult that nobody can't work it out.
    which is ungrammatical (that's what the "*" means).




  2. Everybody, somebody, and anybody are all Quantifiers -- logically, ∀ and ∃.
    By DeMorgan's Laws, propositions with both a negative and a quantifier are ambiguous.



    Note the opposite orders of not (logically ¬),
    compared to some/any (∃) and every (∀) below.



    I.e, Everybody doesn't like it
    can mean either
    It is true that there is somebody who does not like it.
    ¬(∀x) φ(x) ≡ (∃x) ¬φ(x)
    or
    It's not true that there is somebody who likes it.
    ¬(∃x) φ(x) ≡ ∀(x) ¬φ(x)




So the two choices that are grammatical do not mean the same thing.



  • The test is too difficult for everybody to figure out means
    'The test is so difficult that there are some people who can not figure it out'

  • The test is too difficult for anybody to figure out means
    'The test is so difficult that there are no people who can figure it out'


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