Let the universe of discourse be the set of all human beings. $M(x)$ is an open statement which stands for "x is a man" and $B(x)$ stands for "x has black hair".
I have problem understanding how the statement $\neg(\forall x)(M(x) \rightarrow B(x))$ is different in meaning from $(\forall x)\neg(M(x)\rightarrow B(x))$ in meaning.
Is my understanding correct if I say statement 1 means not every man has black hair and statement 2 means: NO MAN (not human beings) has black hair?
The first statement means that it is not true that every man has black hair
The second statement is equivalent to $\forall x (M(x) \land \neg H(x))$ and thus means that everything in the domain is a man and does not have black hair
I asume you can see the difference now ...