Let C(x) be the statement “x has a cat,” let D(x) be the statement “x has a dog,” and 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. Let the domain consist of all students in your class.

No student in your class has a cat, a dog, and a ferret.



The statement "No student in your class has a cat, a dog, and a ferret" can be expressed logically using quantifiers, logical connectives, and the given predicates \( C(x) \), \( D(x) \), and \( F(x) \).

Let the domain of discourse consist of all students in your class. The formal expression for this statement is:

\[
\neg \exists x (C(x) \land D(x) \land F(x))
\]

### Explanation:
- \( \exists x \) means "there exists a student \( x \)".
- \( C(x) \land D(x) \land F(x) \) means "student \( x \) has a cat, a dog, and a ferret".
- The negation \( \neg \) in front of the existential quantifier indicates that "no student" has all three pets.

Thus, the expression \( \neg \exists x (C(x) \land D(x) \land F(x)) \) translates to "There does not exist a student \( x \) who has a cat, a dog, and a ferret," which matches the original statement.

Would you like a detailed breakdown of how this logic works or clarification on any part of the explanation?

Here are 5 related questions to expand your understanding:

1. How would you express the statement "Every student in the class has at least one pet" using quantifiers?
2. What is the logical form of the statement "Some student in the class has a cat but not a dog"?
3. How would you express "At least one student has either a cat or a dog but not both"?
4. How can you write "No student has a dog but at least one student has a ferret" using these predicates?
5. How would you express "All students in the class have either a dog or a ferret, but not both"?

**Tip**: In logic, negations of existential and universal quantifiers switch their roles. For example, \( \neg \exists x P(x) \) becomes \( \forall x \neg P(x) \), and vice versa.

Let C(x) be the statement 'x has a cat,' let D(x) be the statement 'x has a dog,' and 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. Let the domain consist of all students in your class. No student in your class has a cat, a dog, and a ferret.

Learn how to express the logical statement 'No student has a cat, a dog, and a ferret' using quantifiers and logical connectives. This solution covers key concepts in logic such as predicates, conjunctions, and negation of existential quantifiers. Suitable for undergraduate students in introductory logic or discrete mathematics courses.

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