Question: Prove that (a) (L + M) = L + M , (b) (cL) = cL for c R, (c)

Prove that 

(a) (L + M)∗ = L∗ + M∗,

(b) (cL)∗ = cL∗ for c ∈ R,

(c) (L∗)∗ = L, 

(d) (L − 1)∗ = (L∗) − 1.

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