6. Let = {a,b,c} and let Σ* be the set of all words wusing letters from EΣ; 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.

Answered: 6. Let (a, b, c) and let Σ* be the set…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

6. Let = {a,b,c} and let Σ* be the set of all words w
using letters from EΣ; 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.

Expert Solution

Step 1

One to one function: A function f is one-to-one if all element of the range of f corresponds to exactly one element of the domain of f. It is also called as injective function.

Consider f: S $\to$ S. The function is said to be injective if for all x and y in S, when f(x)=f(y) $\Rightarrow$ x=y

or, if x ≠ y $\Rightarrow$ f(x) ≠ f(y).

Onto function: A function f: X $\to$ Y is onto function if every element of set Y has a preimage in X or $\forall$ y $\in$ Y and $\exists$ x $\in$ X such that f(x)=y.