Aug2016 cs Q70

0. 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. ∀x ν(x ) ⇔ (∀y e(x, y) ⇒ ¬m(y))
II. ∀x ν(x ) ⇔ (¬(∃y m(y) ∧e(x, y)))
III. ∀x (∃y m(y) ∧e(x, y)) ⇔ ¬ν(x)
One can determine that

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