I was reading a book where the author converts the sentence
Everyone who loves all animals is loved by someone
to this logical sentence:
∀x [∀y Animal(y) => Loves(x, y)] => [∃z Loves(z, x)
However I came up with this logic, which's different:
∀x [∀y Animal(y) ∧ Loves(x, y)] => [∃z Loves(z, x)]
Note however that the next sentence, is converted similar to second version one instead of the first version. So going by the previous example, why is the sentence
Anyone who kills an Animal is loved by no one
converted to
∀x [∃y Animal(y) ∧ Kills(x, y)] => [∀z ¬Loves(z, x)]
instead of this:
∀x [∃y Animal(y) => Kills(x, y)] => [∀z ¬Loves(z, x)
I'm confused as to why we pick one over the other. Can anyone please explain this?