Express each of these statements in terms of C(x), D(x), F(x), quantifiers, and logical connectives

Question

Let C(x) be the statement “x has a cat,” let D(x) be the statement “x has a dog,” let F(x) be the statement “x has a ferret.” Express each of these statements in terms of C(x), D(x), F(x), quantifiers, and logical connectives.

Q1. For each of the three animals, cats, dogs, and ferrets, there is a student in your class who has this animal as a pet.

With full Explanation?

ans = ∃x (C(x)) ∧ ∃y (D(y)) ∧ ∃z (F(z)) is this correct? if Yes how?

Answer 1

your answer is not correct because you have not formalized ' x has y as pet' and 'x is student'. You need a 2-place predicate to formalize it. The next point is about choosing appropriate quantifiers for 'each'. In this context 'each' is not the same as 'there is'. Once you choose the right quantifiers, then you will find the correct structure of your formula, it should be a conditional.