Regular Language

Question

Given two languages L1 = Φ and L2 = {a}. What is the representation of L1L2*UL1*?

Comments

is the answer epsilon?

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it will be {epsilon}..

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I think that too. Can you explain?

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Φa* union Φ*

Φ union {epsilon}

{ } union {epsilon}= {epsilon}

Answer 1

L1 = Φ and L2 = {a}

L1L2*UL1*

Φ a* U Φ*

Φ U ɛ

{ɛ}

Comments

shouldn't Φ U ε be {ε}, because Φ is an empty set, Φ is not an element?

Answer 2

Phi.a* U phi*

=Phi U epsilon

=Epsilon