Its not then

Its if and only if

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

2 votes

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.

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**