While function how do I use both & and | - while-loop

Question

I am a total noob so when I explain simple stuff, it's not because I'm retarded, it's just that I want to know if I think wrong or right.
I have 2 variables at first, x1 and y1. I put them in a while () like this
while ( y1<0 || y1>500 || x1<0 || x1>500)
I read this as "when one of these "things" are true, it will do the while function.
So for example if y1=601, y1>500 is true, the other 3 are false but it goes into the function since only 1 need to be true.
Now here's where I get problem, I want to add a third variable called z. I add it like this:
while(y1<0 || y1>500 || x1<0 || x1>500 && z>51)
What I want this to do is run the while function ONLY if z>51 is true together with at least 1 more function. Or if thats not possible, I want it to run ONLY if z>51 is true. My code is wrong because right now it just continues on forever even if z>51 is false.

Answer 1

If I understand correctly your question, you want:
while((y1<0 || y1>500 || x1<0 || x1>500) && z>51)
In boolean logic, and (also noted ^ or .) has a higher priority than or (also noted v or +).
Which means that:
y1<0 || y1>500 || x1<0 || x1>500 && z>51
is equivalent to
y1<0 || y1>500 || x1<0 || (x1>500 && z>51)
Therefore, you need parenthesis if that's not what you want, exactly like the parenthesis you add when you use + and * in maths.

Answer 2

Alternatively you could check the value of z first and keep the loop unchanged.
if (z > 51) {
while ( [...])
[...]
}
This is slightly different to Maxime's solution as it assumes that the value of z does not matter once you enter the loop. If you on the other hand want to update z and use it as condition to exit the loop then keep it in the while condition.

Answer 3

The 2 checks are separate.
You can't simply write y1<0 || 50051
You have to write (y1<0 || y1>50051)
50051 always evaluates to true hence I assume it would run forever
for your last request
while(z1>51 && y1 >0)