Ytukyg

As the title says, I'm not sure why "Some men have with brown hair" is $exists x(M(x) wedge B(x))$, but "All men have brown hair" isn't $forall x(M(x) wedge B(x))$?

Doesn't $forall x(M(x) wedge B(x))$ read as "For every $x$, $x$ is a man and $x$ has brown hair?" In other words all men have brown hair.

I'm aware that the correct statement is $forall x(M(x) Rightarrow B(x))$, which reads as "For every $x$, if $x$ is a man, then $x$ has brown hair."

$M(x)$ means "$x$ is a man", and $B(x)$ means "$x$ has brown hair."

It seems like you want to read $forall x (M(x)wedge B(x))$ as saying

For all men $x$, it is true that $x$ has brown hair.

Which is different from the following statement:

For all $x$, it is true that $x$ is a man and has brown hair.

The difference is that, in the first statement, $x$ is necessarily a man. In the second statement, we could take $x$ to be a rock*, and we would claim that it is a man with brown hair. The symbol "$forall x$" means that, no matter what we take $x$ to be, the following statement is true of it.

A common thing to write, however, to express the first statement is
$$forall xin M(B(x))$$
where $M$ is the set of all men; this means that we restrict the choice of $x$ to be within this set - although this is the same as
$$forall x(M(x)rightarrow B(x)).$$

(*Of course, when working in logic, there's generally a well-defined sense of what $x$ could be - but here, unless $M(x)$ is true of every $x$, the statements are not interchangeable - and, speaking informally, it's unlikely that $x$ is implicitly understood to be a man)

It's ultimately a matter of what you're trying to imply.

To say there are some men with brown hair means that both conditions hold true; there exists a person who is both male ($M(x)$) and has brown hair ($B(x)$).

However, think about what it says to say "all men have brown hair." "All men have" is basically saying "$M(x) Rightarrow text{(something)}$". To say "all men have" something is making an ever-so-subtle assumption that being a man implies something.

Another problem with the use of the "and" operator here is the subtle assumption that the $x$'s you're dealing with are people. To say "$forall x, M(x) wedge B(x)$" makes the implication that all people ($x$) are both male ($M(x)$) and have brown hair ($B(x)$). However, we know there are also women among the $x$'s, so that doesn't work out does it?

It's not as overt as saying "$x$ implies $y$," and in the nuances of the English one would look at them as being logically equivalent; it took me a while to even notice myself the nuance. This is probably where your confusion comes from.