1. Show that =_n is an equivalence relation for each n ∈ N. That is, show that =_n is

(a) reflexive: x =_n x for all x ∈Z;

(b) symmetric: x =_n y implies y =_n x for all x, y ∈ Z; and

(c) transitive: x =_n y and y =_n z imply x =_n z for all x, y, z ∈Z.