Understanding symbolic language of problem, quantificational logic

Question

Hi, i am having trouble interpreting the information contained in the relation R, and how it should be applied to the Ps in this problem:

 

Consider the formula 

∃x∃y∃z(P(x,y)∧P(z,y)∧P(x,z)∧¬P(z,x))

Under each pf these interpretations, is this formula true? In each case, R is the relation corresponding to P.

(a) U = N,   R = {<x,y> : x<y}.

(b) U = N,   R = {<x,x+1> : x≥0}.

 

Does <x,y> refer to the variables x,y or z in each P(a,b), and the :x<y refer to what the relation between these two should be?

I tried something like this for (a) and got:

∃x∃y∃z((x<y)∧(z<y)∧(x<z)∧¬(z<x))

However I'm not sure if this is correct, and I'm not sure how I would do it for (b)