Let be the set of all bit strings of length 10. Let be the relation defined on where two bit strings are related if the third, fourth and last bits are the same. Show that is an equivalence relation and enumerate one bit string from each of the different equivalence classes of .

I've already proven that is an equivalence relation, so don't worry about that half of the question.

The second half is what's giving me trouble. I am not entirely sure of how to do this, though I could guess. Since three bits are the same, are there different equivalence classes of ?

EDIT: Here's my current answer to the second half. Can someone confirm if it works?

1100111110

1100111111

1101111110

1101111111

1110111110

1110111111

1111111110

1111111111