Need help...question no 1 &2....

Exercise 2.13 As in Exercise 2.10, let E be the equivalence relation on P(w) defined by x Ey > ry is finite. 1. Prove that the following table of equations determines a Boolean algebra B = (B, V, A, -, 1, T). B = P(W)/E IDE V LyE = [XUyE IDEALUE = nyE -x]E = WW-TE 1 = OE T = WE Before proving the laws of Boolean algebras, you must show that the operations V. A and - are well-defined by the equations listed above. So part of what you must show is that if a Ex' and y Ey', then (x Uy) E(x'uy'), (any) E(a'ny') and (W - X) E (w - x'). Remark: This is an example of a quotient Boolean algebra. In the literature, it is referred to as P(w)/Finite. 2. Prove that the Boolean algebra B that was defined in part 1 has no atoms