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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

  1. Only $I$ and $II$ are equivalent sentences
  2. Only $II$ and $III$ are equivalent sentences.
  3. Only $I$ and $III$ are equivalent sentence .
  4. $I, II,$ and $III$ are equivalent sentences.
in Discrete Mathematics
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1 Answer

1 vote

I.) If x is vegetarian then all food items he eats must not a meat item
II) If x is vegetarian then there should not at least one mean item that x eats
III) If there exitsts one meat item that x eats then x is not a vegetarian


All these senetences are equivalent

Answer is D

2

Its not then 

Its if and only if


Moreover, Are there $2$ biimplications in the last sentence ?

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