Consider the languages \(L_1\) = Φ and \(L_2\) = {a }. Which one of the…

Key insight: evaluate each part using L1 = ∅ and L2 = {a}.

• L2* = a* = {ε, a, aa, ...}.

• L1 L2* = ∅ · a* = ∅ because concatenating any language with the empty language yields the empty language.

• L1* = ∅* = {ε} since the Kleene star of the empty language contains only the empty string.

• Union: ∅ ∪ {ε} = {ε}.

Answer: {ε}