Logic Translation
1. The problem asks to translate logical statements into English, where $R(x)$ means "$x$ is a rabbit" and $H(x)$ means "$x$ hops", with the domain being all animals.
2. For statement (a) $\forall x (R(x) \to H(x))$: This means "For every animal $x$, if $x$ is a rabbit, then $x$ hops." In other words, all rabbits hop.
3. For statement (b) $\forall x (R(x) \wedge H(x))$: This means "For every animal $x$, $x$ is a rabbit and $x$ hops." In other words, every animal is a rabbit and hops.
4. For statement (c) $\exists x (R(x) \to H(x))$: This means "There exists at least one animal $x$ such that if $x$ is a rabbit, then $x$ hops." This is logically weaker than (a) because it only requires one animal for which the implication holds.
5. For statement (d) $\exists x (R(x) \wedge H(x))$: This means "There exists at least one animal $x$ such that $x$ is a rabbit and $x$ hops." In other words, there is at least one hopping rabbit.
Final answers:
(a) All rabbits hop.
(b) Every animal is a hopping rabbit.
(c) There is at least one animal for which if it is a rabbit, it hops.
(d) There is at least one hopping rabbit.