8. Let Σ; be alphabets for i = 1, 2, 3, and L; C Σ;, i = 1, 2, 3 be three languages. Prove that (a) L₁ (L2 UL3) = L₁ L2 UL1L3. (b) (L₁L2) L3 ‡ L1L3NL2L3, in general. (c) L₁ (L2 − L3) ‡ L₁L2 – L₁L3, in general. (d) (L₁UL₂)* = (L1L₂)*.

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