I am completely lost on the terminology on this one.

Let $\displaystyle \rho$ be an equivalence relation on a non-empty set X.

Let a $\displaystyle \epsilon$ X. Show that [a$\displaystyle ]_\rho$ $\displaystyle \not=$ $\displaystyle \emptyset$

Here [a$\displaystyle ]_\rho$ := {b $\displaystyle \epsilon$ X | a$\displaystyle \rho$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.