Let S = {0, 1}. List all the strings of length 4 over S that contain three or more 1's. (Enter your answer in set-roster notation.)

Answer 1

Hello Louis!

We want to list every string of length 4 over S which contains three or more 1's. One approach to this problem is to first consider the strings over S with exactly three 1's.

What exactly are these strings? Since the only other element of S is 0, then these are the strings which contains three 1's and one 0. Specifically:

1. 0111
2. 1011
3. 1101
4. 1110

After these strings are considered, we turn our attention to the "or more" part of the question. All that's left are strings of length 4 with four 1's. There is only one possible string that fits this description: 1111.

Now, all that's left to do is list these strings in set-roster notation. You should be able to do this part. As a hint, remember that set-roster notation for the elements a, b, and c should look something like this: {a, b, c}.