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

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}