Subset of a Regular Expression

Question

Consider the regular expression $R=(a+b)^*a(ab)^*+\epsilon$.
Which of the following are possible as subset of $R$?

(i) $(aa)^*$          (ii) $(ba)^*$          (iii) $(aa)^*(ba)^*$

a. $(i)$ and $(ii)$ only

b. $(ii)$ and $(iii)$ only

c. $(i)$,$(ii)$ and $(iii)$

d. None of these.

Comments

C?

All

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Fxplain it

Answer 1

see what the regular expression given is doing. it will generate all string having atleast one a and it will also generate null. now all option are either generating null or the minimum instance is containing an a. so the condition atleast on a will get satisfied so all are subsets.

Answer 2

The given regular expression can generate empty string or a string containing a.
(aa)* - This can be generated by the given regular expression.
(ba)* -  This could also be generated by the given regular expression.
(aa)*(ba)* - This could also be generated by the given regular expression.

Therefore, all are possible. So. option C is correct.

Answer 3

all are possible what is your answer