Kenneth Rosen Edition 7 Exercise 1.4 Question 8 (Page No. 53)

Question

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.

1. $\forall x (R(x) \rightarrow H(x))$
2. $\forall x (R(x) \wedge H(x))$
3. $\exists x (R(x) \rightarrow H(x))$
4. $\exists x (R(x) \wedge H(x))$

Comments

Should be C right?

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those are not options... you have to represent each statement in First order logic form

Answer 1

1. ∀x(R(x) →H(x))  All rabbit hops.

2. ∀x(R(x)∧H(x))    All animals are hopping rabbits.

3. ∃x(R(x)→H(x))  There exists an animal that, if it is a rabbit then it hops.

4. ∃x(R(x)∧H(x))   Some rabbits hop. 

                              Another way: "There exists an animal that is a rabbit and hop. "