Which two of the following four regular expressions are equivalent? (ε is the empty string).
(i). (00)*(ε+0)
(ii). (00)*
(iii). 0*
(iv). 0(00)*
(A) (i) and (ii)
(B) (ii) and (iii)
(C) (i) and (iii)
(D) (iii) and (iv)
Answer: (C)
Explanation: Here,
(00)*(ε+0)
= (00)*.ε+ (00)*.0
= (00)* + (00)*0
= 0*
It is equal to (iii) [ using regular expression properties ].
Here,
we see that (00)* generates strings of even length and (00)*0 generated the strings of odd length.
Option (C) is correct.
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