Test by Bikram | Theory of Computation | Test 1 | Question: 11

Question

Identify the Regular Expression among the following which denotes ALL strings of $a$'s and $b$'s, where each string contains at least $2$ $b$'s:

• A. $(a+b)^*ba^*b$
• B. $(a+b)^*ba^*ba$
• C. $(a+b)^*ba^*b(a+b)^*$
• D. $(a+b)^*ab^*ab$

Comments

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Sir, A and B can also generate atleast 2 b's ?

Answer 1

(C) is correct answer because it can generate required language, every string which belongs to (a+b)* and contains at least 2 b's.

Comments

1,2,3 all can generate strings of 2b's ?? i didnt get the point plzz explain.

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they should generate all possible strings which contain an 2 b's as substring. in option Aand B you can find some missing strings

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Can you name the missing strings ? a , b ,c has min length as bb , how are you understanding , some strings will be missing ?

Answer 2

Contain at least 2b

option(A):All string must end with b.

option(B) :All string must end with a.

option(D) :All string must end with b.

But our condition is that it must contain at least 2b which may end with a or b.So a,b,d eliminated.

at least 2b i.e may start with a or b i.e (a+b)*

then our condition two bb and it may contain a in between so (a+b)*ba*b

and it may end with a or b that lead to (a+b)*ba*b(a+b)*

So Option C is answer.