Question

How many strings of length five are in the set corresponding to the regular expression (01)*1?

Answer 1

The regular expression (01)*1 represents a pattern of 0s followed by one 1 or an empty string. There are 54 different strings of length five that are in the set corresponding to this regular expression.

Step-by-step explanation:

The regular expression (01)*1 represents a pattern that consists of 0s followed by one 1 or an empty string. To find the number of strings of length five that corresponds to this regular expression, we can consider each position in the string:

1. Position 1: It can be either 0 or 1, so there are 2 possibilities.
2. Position 2: It can be either 0, 1 or an empty string, so there are 3 possibilities.
3. Position 3: It can be either 0, 1 or an empty string, so there are 3 possibilities.
4. Position 4: It can be either 0, 1 or an empty string, so there are 3 possibilities.
5. Position 5: It must be 1, so there is only 1 possibility.

By multiplying the number of possibilities in each position, we get a total of 2 * 3 * 3 * 3 * 1 = 54 different strings of length five that are in the set corresponding to the regular expression (01)*1.