I am completely lost on the terminology on this one.

Let be an equivalence relation on a non-empty set X.

Let a X. Show that [a

Here [a := {b X | a b}

Is this supposed to be b=a? What is this set X?

The only thing I get is that X is non-empty so it must contain at least one element b. Then the equivalence relation has to be non-empty by definition of equivalence.