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# a) Give an example to show that the inclusion in part (b) ISBN: 9780073383095 37

## Solution for problem 41E Chapter 2.3

Discrete Mathematics and Its Applications | 7th Edition

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Problem 41E

a) Give an example to show that the inclusion in part (b) in Exercise 40 may be proper________________b) Show that if f is one-to-one, the inclusion in part (b) in Exercise 40 is an equality.Let f be a function from the set A to the set B. Let S be a subset of B. We define the inverse image of S to be the subset of A whose elements are precisely all pre-images of all elements of S. We denote the inverse image of S by f-l (S). so f-1(S) {a.? A| f (a) ? S}. (Beware: The notation f-1 is used in two different ways. Do not confuse the notation introduced here with the notation f-1(y) for the value at y of the inverse of the invertible function f. Notice also that f-1(S), the inverse image of the set S, makes sense for all functions f, not just invertible functions.)

Step-by-Step Solution:

SolutionStep 1In the problem we have to show the inclusion part of f(S T) f (S) f(T)Let S = {3} and T = { 4} and f(3) = 5, f(4) = 5Then first we have to evaluate intersection of S and T Intersection of S and T = { }So, f(S) = {5} and f(T) = {5}Then, f (S) f(T) = {5} {5} = {5}f(S T) f (S) f(T)Hence, it is proved that it may be proper.

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##### ISBN: 9780073383095

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. This full solution covers the following key subjects: Inverse, set, notation, image, part. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The full step-by-step solution to problem: 41E from chapter: 2.3 was answered by , our top Math solution expert on 06/21/17, 07:45AM. The answer to “a) Give an example to show that the inclusion in part (b) in Exercise 40 may be proper________________b) Show that if f is one-to-one, the inclusion in part (b) in Exercise 40 is an equality.Let f be a function from the set A to the set B. Let S be a subset of B. We define the inverse image of S to be the subset of A whose elements are precisely all pre-images of all elements of S. We denote the inverse image of S by f-l (S). so f-1(S) {a.? A| f (a) ? S}. (Beware: The notation f-1 is used in two different ways. Do not confuse the notation introduced here with the notation f-1(y) for the value at y of the inverse of the invertible function f. Notice also that f-1(S), the inverse image of the set S, makes sense for all functions f, not just invertible functions.)” is broken down into a number of easy to follow steps, and 151 words. Since the solution to 41E from 2.3 chapter was answered, more than 391 students have viewed the full step-by-step answer.

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a) Give an example to show that the inclusion in part (b)

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