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UGC-NET | UGC NET CS 2016 Aug – III | Question 70

  • Last Updated : 12 Apr, 2018

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
(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)


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