Ambiguous Quantifiers

Question

i wondered what kind of quantifiers do not involves ambiguous reading ?

Answer 1

1. is True: pick $x = Andy$ and $y = Ben$:

Andy likes Ben, so

$$like(a,b) = True$$

, and so

$$like(a, b) \lor \neg linguist(a) = True$$

as well.

Also: Ben is taller than Andy, so

$$taller(b,a) = True$$

, and so

$$(like(a, b)\lor \neg linguist(a))\land taller(b,a) = True$$

, and so

$$∃x∃y((like(x, y)\lor \neg linguist(x)) \land taller(y,x)) = True$$

For 2 you got the right answer

3. is True:

Consider Chris: everyone likes Chris, and so

for any $z$, $like(z,c) = True$

Therefore, for any $z$, $Tall(c) \rightarrow like(z,c) = True$

and so

$$\forall z (Tall(c) \rightarrow like(z,c)) = True$$

and thus

$$\neg \forall z (Tall(c) \rightarrow like(z,c)) = False$$

and therefore

$$\exists y (taller(y,x) \lor like(c,y)) \land \neg \forall z (Tall(c) \rightarrow like(z,c)) = False$$

and therefore

$$\forall x (\exists y (taller(y,x) \lor like(c,y)) \land \neg \forall z (Tall(c) \rightarrow like(z,c))) = False$$

and therefore

$$\neg \forall x (\exists y (taller(y,x) \lor like(c,y)) \land \neg \forall z (Tall(c) \rightarrow like(z,c))) = True$$