Let ?: G X ! X be an action of a group G on a set X. Define a binary relation on X by

:= (x; y) 2 X X j y = g ? x for some g 2 G :

True or false?

(a) For every x 2 X we have x = e ? x.

(b) If y = g ? x, then x = g-1 ? y.

(c) If y = g ? x and z = h ? y, then z = hg ? x.

(d) is not an equivalence relation