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Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 2.se - Problem 15e
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 2.se - Problem 15e

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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 2 of 3

Step 3 of 3

##### 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 305 students have viewed the full step-by-step answer.

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