Hi. I have this problem to solve:

(∀x(P(x,x)∧∀x∀y∀z[(P(x,y)∧P(y,z))→P(x,z)]∧∀x∀y[P(x,y)∨P(y,x)])→∃y∀xP(y,x).

In natural language this means that if a relation P is reflexive and transitive and for two elements a,b we have P(a,b)∨P(b,a) then there is another element d in the universe that for every other element c of the universe we have P(d,c).

Here is the first question:

Give an interpretation that is no model of the above type. Seek an interpretation in an infinitive universe. The universe could be the natural numbers and the interpretation some known relation among the natural numbers.

Some help ?? Thank you.