Thread: Show that R is an equivalence relation

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

Hello, Runty!

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.

a) Show that is an equivalence relation.

(b) Enumerate one bit string from each of the different equivalence classes of .

You are right . . . There are 8 equivalence classes.

And they look like this:

. .


And the blanks can be filled with any combination of 0's and 1's.