Equivalent RelationsLet S and S′ be the following subsets of the plane:(a) Show that S′ is...

Equivalent Relations

Let S and S′ be the following subsets of the plane:

(a) Show that S′ is an equivalence relation on the real line and S′ ⊃ S. Describe the equivalence classes of S′.

(b) Show that given any collection of equivalence relations on a set A. their intersection is an equivalence relation on A.

(c) Describe the equivalence relation T on the real line that is the intersection of all equivalence relations on the real line that contain S. Describe the equivalence classes of T.