Question

The regular expression of the language \(\{0, 01, 011, 0111, \dots\}\) is given by:

• A. \( (0 + 1)^* \)
• B. \( (01)^* \)
• C. \( (0)(A)^* \)
• D. \( 01^* + 0 \)

Hint:

A regular expression describes a set of strings using symbols and operators:
- \( a^* \) means "zero or more occurrences of 'a'".
- \( (a + b) \) means "either 'a' or 'b'".
- \( (a)(b) \) ensures 'a' is followed by 'b'.

Answer 1

The Correct Option is C

Step 1: Understanding the Given Language The given language consists of strings: \[ 0, 01, 011, 0111, \dots \] Observing the pattern, we see that:
- Every string starts with '0'.
- It may be followed by any number of '1's (including zero occurrences of '1').
Step 2: Evaluating the Given Options
- Option (A) \( (0 + 1)^* \): This includes all possible combinations of '0' and '1', which is too general.
- Option (B) \( (01)^* \): This allows only even-length strings where '0' and '1' alternate, which does not fit the given language.
- Option (C) \( (0)(A)^* \): This correctly represents the pattern where '0' is followed by any number of '1's.
- Option (D) \( 01^* + 0 \): This is another way to express the same concept but does not follow standard regular expression representation.
Step 3: Conclusion
Since \( (0)(A)^* \) correctly captures all valid strings in the given language, option (C) is the correct answer.