Translate these statements into English, where R(x) is “x is a rabbit” and H(x) is “x hops” and the domain consists of all animals.
∀x(R(x) ∧ H(x))


The given statement is:

\[
\forall x (R(x) \land H(x))
\]

This translates to:

"All animals are rabbits and hop."

Here, \( \forall x \) means "for all \( x \)" (where \( x \) represents any animal in the domain), \( R(x) \) means "x is a rabbit," and \( H(x) \) means "x hops." The conjunction \( \land \) means "and."

Would you like to explore this further or have any questions? Here are some related questions to think about:

1. How would the statement change if it were \( \exists x (R(x) \land H(x)) \)?
2. What does the statement \( \forall x (R(x) \rightarrow H(x)) \) mean?
3. How would you express "Some animals are rabbits that hop" using the same notation?
4. Can you modify the statement to say "Not all rabbits hop"?
5. What logical formula represents "No rabbits hop"?

**Tip:** Understanding the quantifiers \( \forall \) (for all) and \( \exists \) (there exists) is key in translating logical statements accurately.

Translate these statements into English, where R(x) is 'x is a rabbit' and H(x) is 'x hops' and the domain consists of all animals. ∀x(R(x) ∧ H(x))

This problem focuses on translating the logical expression ∀x(R(x) ∧ H(x)), which states that all animals are rabbits and hop. Learn about universal quantifiers, propositional logic, and logical conjunctions, suitable for students in Grades 10-12.

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