What is negation of the following sentence? What is negation of All birds can fly.

The question seems bit funny but i don't know which of the following two sentences is correct:


Some birds can not fly
There is at least one bird which can not fly.


Both the sentence seems almost logically same. But which of the following is true.

In book correct option out of four is sentence 1.
$B(x):$ x is a bird. 

$F(x):$ x can fly.

All birds can fly: $$\forall x(B(x)\rightarrow F(x))$$

Negation of the above $$\lnot \forall x(B(x)\rightarrow F(x))\equiv \exists x \Big(\lnot\big(\lnot B(x) \lor F(x)\big)\Big) \equiv \exists x (B(x) \land \lnot F(x)$$

You can certainly translate the statement as you did, and your translations are equivalent: mathematically, some is equivalent to at least one. So you may as well stick with "some". 

An alternative translation of the negation would be simply the negation symbolized at the very left: "Not all birds can fly."
I would say only 2 is the negation of All birds can fly.

All birds can fly is only true if all birds can do it.

So if not all birds can fly it would be a negation.

There is at least one bird which can not fly, is equal to not all birds can fly