Question

Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) A(x): x is an animal; B(x): x is a bear; H(x): x is hungry; W(x): x is a wolf. a. Bears are animals. b. No wolf is a bear. c. Only bears are hungry. d. If all wolves are hungry, so are bears. e. Some animals are hungry bears. f. Bears are hungry but some wolves are not. g. If wolves and bears are hungry, so are all animals. h. Some wolves are hungry but not every animal is hungry.

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a.\textbf{a.} Since the sentence talks about all\textbf{all} bears, we will use the universal quantifier. The universal quantifier often goes together with implication.

So, this sentence can be thought of as ``For every being xx, if xx is a bear, then xx is an animal'', which can pretty much directly be translated to:

(x)(B(x)A(x)).\begin{equation*} \textcolor{#c34632}{(\forall x)(B(x)\rightarrow A(x))}\text. \end{equation*}

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