1) Recall that an equivalence relation S on set R ( R being the reals) is a subset of R x R such that
(a) For every x belonging to R (x,x) belongs to S
(b) If (x,y) belongs to S, then (y,x) belongs to S
(c) If (x,y) belongs to S and (y,z) belongs to S then (x,z) belongs to S
What is the...