Let S be a set with a finite number of elements, and let f: S - S be a map _ (a) If fis onto, can If f is 1-1, can f not be onto? Do your conclusions remain valid even if S has an infinite number f not be 1-1? (b) |(c) of elements?

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 29E: 29. Suppose , , represents a partition of the nonempty set A. Define R on A by if and only if there...
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Let S be a set with a finite number of elements, and let f: S - S be a map
_
(a)
If fis onto, can
If f is 1-1, can f not be onto?
Do your conclusions remain valid even if S has an infinite number
f not be 1-1?
(b)
|(c)
of elements?
Transcribed Image Text:Let S be a set with a finite number of elements, and let f: S - S be a map _ (a) If fis onto, can If f is 1-1, can f not be onto? Do your conclusions remain valid even if S has an infinite number f not be 1-1? (b) |(c) of elements?
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