Logic for Computer Science

For each of the following formulas in FOL, give a suitable structure, = (U, I), such that under this structure, (a.1) is false, and (a.2) and (a.3) are true:

(a.1) xyz((P(x,y) P(y,z)) P(x,z))

(a.2) xy((P(x,y) P(y,x)) x = y)

(a.3) xy(P(a,y) P(x,b))