Question

Which of the following is a correct statement?

(a) { If an bn  | n = 0,1, 2, 3 ..} is regular language

(b) Strings with equal number of a’s and b’s denies a regular language

(c) L (A* B*)∩ B gives the set A

(d) None of the mentioned

I had been asked this question during an interview.

This intriguing question comes from The NFA with epsilon topic in section Finite Automata and Regular Expression of Compiler

Answer 1

Right option is (c) L (A* B*)∩ B gives the set A

Best explanation: If we include A and B in a set and if we write A*  it means except  then A i.e. B  same as  B*  means except then B i.e. so if we intersect (A*B*)  and B   then get A  because in any regular language. If we write A-B then A-B=A intersection B’  so if we intersect A and B means A-B  So the intersection of (A*B*) and B  = (BA). intersection B  means (BA)-B’ and B’=A so (BA) intersection(A)=A.