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Consider the languages L1 equal to phi and L2 equal to small A. Which one of the following represents
L1 dot L2 star, union L1 star? Star is nothing but closure. Now
substituting the values we get phi dot L2 star i.e. A star union L1 star i.e. phi star. Now phi dot anything
is nothing but phi, union phi star. At this point everybody would be like "What the hell"
lets go ahead the answer is phi lets mark (B) and get done with it but however we made
a major blunder-we just lost one mark. This is wrong. And why is this wrong? It's because
people tend to forget the important property of closure. For example, 'a' closure is nothing
but epsilon, a, aa and so on. If you notice, the closure always contains an epsilon in
the beginning. Hence, actually speaking, phi star is nothing but epsilon, phi, phi phi
and so on. But this is nothing but phi in itself. This is phi union epsilon phi which
makes it epsilon. And hence the correct answer is set epsilon.
And this is how the derivation looks like.