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Question

Let v(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 v(x) ⇔ (∀y e(x, y) ⇒ ¬m(y))
II. ∀x v(x ) ⇔ (¬(∃y m(y) ˄ e(x, y)))
III. ∀x (∃y m(y) ˄ e(x, y)) ⇔ ¬v(x)

One can determine that

a.

Only I and II are equivalent sentences

b.

Only II and III are equivalent sentences

c.

Only I and III are equivalent sentence

d.

I, II, and III are equivalent sentences

Answer: (d).I, II, and III are equivalent sentences

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Q. Let v(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 v(x) ⇔ (∀y e(x, y) ⇒ ¬m(y)) II. ∀x v(x )...

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