Sep 27th 2014 CSC165 TUT

some questions  that I had already solved  in the TUT
1) " every course has a prerequisite" rewrite it symbolically:
 ∀y∈c, ∃∈x, p(x,y)
∃∈c,∀y∈c,p(x,y)
the order doesn't matter at this sentence ,so it is the same.
2)"some course have several prerequisites"
∃x,y,z∈c, p(x,y)∧p(z,y)∧x!=z
in this translation, "two means several", what we only to do is just define x,z two "courses" which is not the same

3) "there is no prerequisite for CSC108"

¬(∃x∈c,p(x,CSC108) if and only if (i could not find the symbol on internet,but it is the same meaning)∀x∈c,¬p(x,CSC108)

negate the whole sentence needs to change existence to global

However ,there are still some question that I want to figure out.

"Some course have the same prerequisites"

The rewriting of this sentence is 

∀x,y,z,w∈c,(p(x,w)∧p(y,w)∧p(z,w))⇒x=y ∨ x=z∨y=z

I could understand the meaning, however, why we need to use x,y,z to represent "some "prerequisite?

In my opinion, I could just only use x, y just like following:

 ∀x,y,w∈c,(p(x,w)∧p(y,w))⇒x=y

Isn't it still represent the same meaning?Or, this sentence only means that "if x,y are prerequisites of course w, then x is equal to y" and this meaning nothing because it is always right?