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Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 2.se - Problem 14e
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 2.se - Problem 14e

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# Suppose that f is a function from A to B where A and B are

ISBN: 9780073383095 37

## Solution for problem 14E Chapter 2.SE

Discrete Mathematics and Its Applications | 7th Edition

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Problem 14E

Suppose that f is a function from A to B where A and B are finite sets. Explain why | f(S )| ? | S | for all subsets S of A.

Step-by-Step Solution:

SolutionStep 1Proof by ContradictionLet us assume that S be a subset of A.By Contradiction, |f[S]| > |S|Now we have to define a function x : f(S) S by x(b) = some a belong to x like that f(a) = b.Pigeonhole PrincipleIf A and B are finite sets then |A| > |B| then f will not be an onto function.According to the pigeonhole Principle, if some ‘a’ belong to x and ‘b’ belongs to f[x]. Thenx(b) = x(b’) = aSo, if f(a) = b and f(a) = b’ Here, f be a onto function then |f(a)| bHence, by contradiction it is proved that |f(S)| |S| for all subset of A.

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##### ISBN: 9780073383095

Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. This full solution covers the following key subjects: explain, Finite, function, Sets, Subsets. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The answer to “Suppose that f is a function from A to B where A and B are finite sets. Explain why | f(S )| ? | S | for all subsets S of A.” is broken down into a number of easy to follow steps, and 32 words. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. Since the solution to 14E from 2.SE chapter was answered, more than 396 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 14E from chapter: 2.SE was answered by , our top Math solution expert on 06/21/17, 07:45AM.

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