Finite Automata: Regular Expressions

Let L₁ and L₂ be any regular expressions. For each identity below, decide True or False.\

(a) (L₁ L₂)* = L₁* L₂*

(b) (L₁L₂ L₁)*L₁ = L₁(L₂L₁ L₁)*

(c) (L₁L₂ L₁)*L₁L₂ = L₁(L₁L₁*L₂)*

(d) (L₁ L₂)*L₂ = (L₁*L₂)*

(e) L₂(L₁L₂ L₂)*L_{1 =} L₁L₁*L₂( L₁ L₁*L₂)*