Let S = {1,2,3,4,5,6,7,8,9} and T = {1,2,3,4,5}. Let R be the relation on P (S) defined by: For any X,Y belongs to P(S), XRYlt;=gt;| XT=YT. (a)...

1. Let S = {1,2,3,4,5,6,7,8,9} and T = {1,2,3,4,5}. Let R be the relation on P (S) defined by: 

For any X,Y belongs to P(S), XRY<=>| X∩T｜=｜Y∩T｜.

(a) Prove that R is an equivalence relation.(b) How many equivalence classes are there? Explain.(c) How many elements does [Ø］have? 

(d) How many elements does [T] have?(d) How many elements does [｛1，2｝] have?