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Need help translating this sentence to predicate logic.

If a student brings a candy bar for him or herself, then that student brings a candy bar for everyone.

  • Use $C(w)$ as the one-place predicate "$w$ is a candy bar"

  • Use $B(x, y, z)$ as the three-place predicate "$x$ brings $y$ for $z$"

This is what I have but I am unsure if it's the correct solution $$\exists x(B(x, C(w), x)) \rightarrow \exists x \forall z(B(x, C(w), z))$$

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  • $\begingroup$ I think the first part of the implication must have two possible options: for him or for me. $\endgroup$ – manooooh Sep 21 '18 at 5:42
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You forgot to get any candy bars. Notice that it is the same student each time and $C(x)$ is not a candy bar, it is a statement.

$\exists x (\exists w (C(w) \wedge B(x,w,x)) \rightarrow \forall z \exists w (C(w) \wedge B(x,w,z)))$

That is still incomplete because a predicate $S(z)$ - is a student - needs to be included.
Presumably everyone is just the students in the class and not all the students, teachers, principal and assistants in the school.

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