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Consider the languages L1 = Φ and L2 = {a}. Which one of the following represents L1L2* U L1*?

A {ε}
C a*
D {ε,a)

Answer & Explanation

Answer: Option [A]

L1=Φ. So L1L2*=Φ. Though multiplication of any language with Φ results in Φ.

Again ε∈L1*. So, L1L2* U L1* = ΦUε

Concatenation Φ with anything results in Φ. Though Φ is an empty string.

So, ΦUε = {ε}

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