Predicate logic help please: Nobody loves john?

(Ax)~Lxr or (Ex)~Lxr or ~(Ax) Lxr

I think it's either the first or the second but I don't have an example for nobody.

Is nobody the same thing as no one in logic? (To me they seem like the same thing.)

Thank you for your help!

3 Answers

  • 8 years ago
    Favorite Answer

    You want to hang this on the identity relation from existential to universal quantifiers. In short:

    ∀x(Px) ⇔ ¬∃x(¬Px)

    So take the converse statement "Everyone doesn't love John". Your predicate is "loves John" (L):

    ∀x(¬Lx) can read this as "It is the case that for all things 'x', it is not the case that 'x' Loves John".

    Now invert this by the identity above, "Nobody (or no one) loves John"

    ∴ ¬∃x(Lx) can read this as "It is not the case that there is something 'x' for which something x Loves John"

    For nobody / no one, yes, they are the same, because they do the exact same thing.

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  • 3 years ago

    it quite is a very unhappy subject for you, little question. and because i do no longer understand the full history of what and the style you have dealt with your mum and dad and for how long, i won't be able to truly make a honest evalution. All i can quite say is that in case you disrespect your mum and dad, then they have the wonderful to do the comparable to you. What is going around comes around. additionally do unto others as you've got them do unto you. This in all probability isn't what you're searching for in an answer, yet you're able to deal with human beings perfect for them to be good to you. that's an argument of compromising and getting alongside. it quite is mandatory for a happy family united.

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  • 8 years ago

    Sharpen It hit that one right out of the park. Great answer.

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