Subjects logic

Logical Expression 3Fb072

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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