Aptitude | GATE CS 1998 | Question 9

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


Answer: (D)

Explanation: Some of the regular expression always equivalent to (0+1)* such that

(0+1)* 
= (0*+1*)* 
= (01*)* 
= (0*+1)* 
= (0+1*)* 
= 0*(10*)* 
= 1*(01*)* 

Since,

(01+1)* = ((01)* 1* )*  

Therefore A = B.

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