I need some clarity on predicate logic:
Given D(x) x is a dog F(x, y) x is a friend of y O(x, y) x owns y h Harry s Susan express the following sentence in predicate logic All of Harry's friends are dog owners
My understanding is that a predicate cannot be an argument to another predicate.
This is what I think is the solution
∃x[F(x, h) ∧ ∀x∃y(D(y) ∧ O(x, y))]
Is that valid? To me it reads: Some people are friends of Harry, then that same person definitely own a dog?
Or is the answer the simpler
∀x∀y[F(x, h) ∧ D(y) ∧ O(x, y)]
But it feels like that says everyone is a friend of Harry
After some input from @Keelan:
∀x[F(x, h) → ∃y(O(x, y) ∧ D(y))]
Which I read as: For everyone where it is the case that they are friends with Harry, they own y and y is a dog.