If the regular set 'A' is represented by A= (01+1)* and the regular set 'B' is…
1998
If the regular set 'A' is represented by A= (01+1)* and the regular set 'B' is represented by B= ((01)* 1*)*, which of the following is true ?
- A.
A ⊂ B
- B.
B ⊂ A
- C.
A and B are incomparable
- D.
A = B
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Correct answer: D
To determine the relationship between sets A and B, we analyze their regular expressions. Set A = (01+1)* generates all strings composed of '01' blocks or single '1's. This means every '0' in a string from A must be immediately followed by a '1'.
Set B = ((01)* 1*)* also generates strings where every '0' is followed by a '1'. The inner part (01)* 1* allows any number of '01' pairs followed by any number of '1's, and the outer * repeats this pattern.
Since both expressions enforce the constraint that no '0' can appear at the end or be followed by another '0', they describe the exact same language.
Therefore, A = B.