6. Let (a, b, c) and let Σ* be the set of all words w using letters from Σ; see Example 2(b). Define L(w) = length(w) for all w € Σ*. (a) Calculate L(w) for the words w₁ = cab, ₂ = ababac, and w3 = λ. (b) Is L a one-to-one function? Explain. (c) The function L maps Σ* into N. Does L map Σ* onto N? Explain. (d) Find all words w such that L(w) = 2.

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