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Chapter 1 Exercises Exercise 1 Mappings, etc. The goal of this exercise is to remind the notions of function, injection, surjection, bijection, permutation, and transposition. If any of those notions is not clear to you, keep reading! Consider the two sets X = {xl,xz,. . . , x,) and Y = {yl, y2,. . . , ym), and a function f : X - y. As f is a function, it assigns to each element of X a single element of y. 1 If n < m, can f be a function? What about the case where n > m? 2 Consider the case where n = 3 and m = 4. Which of the following diagrams represent a function? Explain why (or why not). 3 A function f is said to be 1 - 1 (one to one), or injective, if each element of y is the image of at most one element of X, i.e., for all Xl,X2 E X, f (~1) = f (~2) * 21 = 22. 2 EXERCISE BOOK Which of the following diagrams represent an injective function? 4 A function f is said to be surjective if each element of y is the
Published: Jan 1, 2006
Keywords: Block Cipher; Data Encryption Standard; MONDAY Morning; Modular Addition; Perfect Secrecy
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