Student Pets
1. **Problem statement:** Express the statement "A student in your class has a cat, a dog, and a ferret" using the predicates $C(x)$, $D(x)$, $F(x)$, quantifiers, and logical connectives, where the domain is all students in your class.
2. **Formula and explanation:** To say "there exists a student who has a cat, a dog, and a ferret," we use the existential quantifier $\exists$ and the logical AND connective $\wedge$ to combine the predicates:
$$\exists x (C(x) \wedge D(x) \wedge F(x))$$
This means there is at least one student $x$ such that $x$ has a cat, $x$ has a dog, and $x$ has a ferret.
3. **Intermediate work:** No further simplification is needed since the statement is already in its simplest logical form.
4. **Explanation:** The existential quantifier $\exists x$ means "there exists at least one $x$ in the domain." The conjunction $\wedge$ means "and." So the whole statement says "there exists a student $x$ such that $x$ has a cat AND $x$ has a dog AND $x$ has a ferret."
**Final answer:**
$$\exists x (C(x) \wedge D(x) \wedge F(x))$$