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.
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|...
Textbook: Discrete Mathematics and Its Applications
Author: Kenneth Rosen
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 297 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.