Let Σ = {a, b}. Define: R₁ = (a + b) b (a + b)
Let Σ = {a, b}. Define:
R₁ = (a + b) b (a + b)
R₂ = (a + b) a (a + b)
R₃ = (a + b) b (a + b)**
R₄ = (a + b) (aa + bb) (a + b)*
Define F(R) as the language denoted by R using the usual recursive rules:
F(a) = {a}, F(b) = {b}, F(ε) = {ε}
F(R1 + R2) = F(R1) ∪ F(R2)
F(R1R2) = F(R1) · F(R2)
F(R)* = (F(R))*
Which of the following statements about the equivalence of these regular expressions is true?
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Correct answer: (C) F(R₃) = Σ* \ a*