Question

a. A function f: A B is called injective or one-to-one if whenever f (x) f(u) for some z, y A then y. Which of the following functions are injective? In r-y. That is Vr,y E A f()-f(u) each case explain why or why not i. f:Z Z given by f(z) 3 7 ii. f which maps a QUT student number to the last name of the student with that student number. b. Suppose that we have some finite set S and we have put them into a list, s1,s2,..., sn (where n ISI). We will argue that the list produces a topological ordering on S. To do this we first define f: S → Z where f(si) f(s2)- 2 and in general f(s,)-j. i. Argue that f is injective ii. Define a relation R on S by aRb whenever f(a) s f (b). Argue that R is a total ordering on R by showing that R is reflexive, anti-symmetric, transitive, and has the total ordering property: Va,ye S aRy V yRz Vz y. (Hint: you will need to use the fact that f is injective to show that R is anti-symmetric.)

Answer 1

廿1 つ otiven o Student Namc om Jeh Jah 02

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