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# Suppose that is a function from A to B where A and If are ISBN: 9780073383095 37

## Solution for problem 15E Chapter 2.SE

Discrete Mathematics and Its Applications | 7th Edition

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Problem 15E

Suppose that is a function from A to B where A and If are finite sets. Explain why | f(S) | = | S | for all subsets S of A if and only if f is one-to-one.Suppose that f is a function from A to B. We define the function Sf from p(A) to p(B) by the rule Sf(X) = f(X) for each subset X of A. Similarly, we define the function Sf?1 from p(B) to p(A) by the rule Sf?1(Y) = f?1(Y) for each subset Y of B. Here, we are using Definition 4, and the definition of the inverse image of a set found in the preamble to Exercise 42, both in Section 2.3.

Step-by-Step Solution:

SolutionStep 1In this problem, we have to show that function A to B where A and B finite sets.and we have to explain that why f(S) = |S| for all subsets S to A if and only if f is one to one function.Step 2One to one functionA function is said to be one to one if and if one object of the domain have exactly one range of that object.Bijective functionThe function is said to be bijective if and only if each object of one set is joined with exactly one object of the other set and vice versa.CardinalityIt is the number of element in a set.Step 3Proof by contradictionLet us assume that f is onto function then by the pigeonhole...

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##### ISBN: 9780073383095

This full solution covers the following key subjects: function, subset, definition, suppose, rule. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The full step-by-step solution to problem: 15E from chapter: 2.SE was answered by , our top Math solution expert on 06/21/17, 07:45AM. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. The answer to “Suppose that is a function from A to B where A and If are finite sets. Explain why | f(S) | = | S | for all subsets S of A if and only if f is one-to-one.Suppose that f is a function from A to B. We define the function Sf from p(A) to p(B) by the rule Sf(X) = f(X) for each subset X of A. Similarly, we define the function Sf?1 from p(B) to p(A) by the rule Sf?1(Y) = f?1(Y) for each subset Y of B. Here, we are using Definition 4, and the definition of the inverse image of a set found in the preamble to Exercise 42, both in Section 2.3.” is broken down into a number of easy to follow steps, and 117 words. Since the solution to 15E from 2.SE chapter was answered, more than 246 students have viewed the full step-by-step answer.

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