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!
- sharpen it.Lv 58 years agoFavorite 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):
...you 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"
...you 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.
- bonagurioLv 43 years ago
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- bonshuiLv 68 years ago
Sharpen It hit that one right out of the park. Great answer.