Predicate calculus- meaning of the word "any" In the following 2 statements -

1. Anyone who eats any pumpkin is a nutrition fanatic. 
&amp;forall x ((&amp;exist y (PUMPKIN(y) &amp;and EAT(x,y))) &amp;rarr FANATIC(x))

2. Anyone who buys any pumpkin either carves it or eats it. 
&amp;forall x &amp;forall y (PUMPKIN(y) &amp;and BUY(x,y) &amp;rarr CARVE(x,y) &amp;or EAT(x,y))


In the first case any pumpkin is given by &amp;exist and 

in the second case any pumpkin is given by &amp;forall

Why the second case is also not given by &amp;exist?
So I am assuming your question is: Why is the formula to "Anyone who buys any pumpkin either carves it or eats it."

$\forall x \forall y (\text{pumpkin}(y) \wedge \text{buy}(x, y) \implies \text{carve}(x, y) \vee \text{eat}(x, y)) $

instead of 

$\forall x \exists y (\text{pumpkin}(y) \wedge \text{buy}(x, y) \implies \text{carve}(x, y) \vee \text{eat}(x, y)) $

The problem with your version is that there might be someone who buys a pumpkin and decides not to eat or carve it and this would contradict the statement that every bought pumpkin (by a person $x$) will be either carved or eaten.