Can someone explain the solution to this statement? Say C: set of courses
P(x,y): 'x is a prerequisite for course y'
statement: 'some courses have several prerequisites'
symbolically: 
 ∃ x ∈ C, ∃ y ∈ C, ∃ z ∈ C, P(y, x) ∧ P(z, x) ∧ y ≠ z

I don't really understand how you get the symbolic expression from the verbal expression. 
Also, might there be a simpler way of writing this in logical notation?
In addition!
How would you write this:
No course has more than two prerequisites.

Thank you.

"Some courses have several prerequisites"
$\Rightarrow$ " $\exists x \in C$ such that $x$ has several prerequisites"
$\Rightarrow$ " $\exists x \in C$ such that $x$ has at least two different prerequisites"
$\Rightarrow$ " $\exists x \in C$, $ \exists y, z \in C$ such that $y \neq z$, $P(y, x) \wedge P(z, x)$ "
$\Rightarrow$ $\exists  x, y, z \in C$,  $y \neq z$, $P(y, x) \wedge P(z, x)$ "
For the second part, using similar reasoning we can symbolically write :
$\nexists x, y, z, w \in C$, $P(y,x) \wedge P(z, x) \wedge P(w, x) \wedge y \neq z \neq w $
