Logic and Quantifiers, simple discrete math question

Question

I'm a couple of weeks into a discrete mathematics course now, and there's one thing I just can't seem to wrap my head around. Here's my problem:

Lets say $C(x)$ means "$x$ is in my class", and $M(x)$ means "$x$ has seen a movie".

Now if I wanted to express that every $x$ that is in my class has seen a movie, I would write $$\forall x(C(x)\to M(x)).$$ Now my question is, why can't I write $$\forall x(C(x)\land M(x)).$$ I can tell this is simple, but please help me out.

Answer 1

"C(x) and M(x)" says that everyone in the world is both in your class and has seen the movie. The implication says should we select an arbitrary classmate, they will have seen the movie.