Regular Expressions - Is this solution correct?

Question

Q. Consider following Regular Expression:
(i) a*b*b (a+ (ab)*)* b*
(ii) a*(ab + ba)* b*
What is length of shortest string which is in both (i) & (ii)?
(a) 2
(c) 4
(b) 3
(d) None

Solution: Option (d)

Explanation:
The shortest string is ε generated by both the regular expressions

I believe the above explanation is wrong as (i) will generate at least 'b'.

Please correct me if I'm wrong.

Comments

It is asking for both not only for 1st.Both Answer and explanation are right.

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The explanation says $\epsilon$ is the shortest string generated by both Regular Expressions. But I think, the shortest string generated by (i) is 'b', not epsilon.

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yes,b is the smallest string derived from both languages.not epsilon.I didn't see properly.

Answer 1

@Akash Mishra...i think u r right....

Q. What is length of shortest string which is in both (i) & (ii)? ....

:_) for the first RE....smallest string is  'b' which is also present in second RE....

hence ...answer i.e (length of smallest string present in both should be '1' ....which is not in the option hence 

option D

Comments

@hs_yadav

you are great!!!!!