1. **State the problem:** We need to express the statement "some student in your class has a cat and a ferret, but not a dog" using logical quantifiers and predicates.
2. **Understand the predicates:**
- $C(x)$ means "x has a cat."
- $D(x)$ means "x has a dog."
- $F(x)$ means "x has a ferret."
3. **Understand the domain:** The domain is all students in your class.
4. **Translate the statement:** "Some student" means there exists at least one student $x$ such that the conditions hold.
5. **Conditions:** The student has a cat and a ferret, but not a dog. This translates to:
$$C(x) \wedge F(x) \wedge \neg D(x)$$
6. **Combine with existential quantifier:**
$$\exists x (C(x) \wedge F(x) \wedge \neg D(x))$$
7. **Check the options:**
- A) $\exists x (C(x) \wedge F(x) \wedge \neg D(x))$ matches exactly.
- B) $\forall x (C(x) \wedge F(x) \wedge \neg D(x))$ means all students have these properties, which is not correct.
- C) $\exists x (C(x) \wedge F(x) \vee \neg D(x))$ is incorrect because the disjunction changes the meaning.
- D) $\forall x (C(x) \wedge F(x) \wedge D(x))$ means all students have cat, ferret, and dog, which is incorrect.
**Final answer:** A
Logical Expression 3Fb072
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