Let $ν(x)$ mean $x$ is a vegetarian, $m(y)$ for $y$ is meat, and $e(x, y)$ for $x$ eats $y$. Based on these, consider the following sentences :
I. $\forall x \vee (x)\Leftrightarrow (\forall y e(x, y) \implies \neg m(y))$
II.$\forall x \vee (x)\Leftrightarrow (\neg(\exists y m(y)\wedge e(x, y)))$
III.$\forall x (\exists y m(y)\wedge e(x, y)) \Leftrightarrow (x)\Leftrightarrow \neg \vee (x)$
One can determine that
- Only $I$ and $II$ are equivalent sentences
- Only $II$ and $III$ are equivalent sentences.
- Only $I$ and $III$ are equivalent sentence .
- $I, II,$ and $III$ are equivalent sentences.