Set partition of strings by suffix

Question

I have this question:

Is this collection of subsets a partition on the set of bit strings of length 8:

The set of bit strings that end with 111, the set of bit strings that end with 011, and the set of bit strings that end with 00.

My answer would be no, this is not a partition, as it does not accommodate strings that end in 10 or 01 for example. However, it appears that I am incorrect based on the given answer. Is anyone able to explain to me why I am wrong?

Answer 1

In this case, you are not wrong, for exactly the reason you stated; the purported partition does not contain e.g. 00000001.

Cheers.