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Can u please explain to me how is number 1 differ from a relation? Please don’t do the prove because I don’t need it, just explain how is it differ from a relation! Thank you my teacher wants me to think about the implications of number 1 so please help. Again NO PROOF NEEDED, I just want an explanation of how does number 1 differ from a relation?

Can u please explain to me how is number 1 differ from a relation? Please don’t do the prove because I don’t need it, just explain how is it differ from a relation! Thank you my teacher wants me to think about the implications of number 1 so please help. Again NO PROOF NEEDED, I just want an explanation of how does number 1 differ from a relation?

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 22E: A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which...
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Can u please explain to me how is number 1 differ from a relation? Please don’t do the prove because I don’t need it, just explain how is it differ from a relation! Thank you my teacher wants me to think about the implications of number 1 so please help. Again NO PROOF NEEDED, I just want an explanation of how does number 1 differ from a relation?
10:53 1 Functions In Section 1.2 we showed that ordered pairs can be defined in terms of sets and we defined Cartesian products in terms of ordered pairs. In this section we introduced relations as subsets of Cartesian products. Thus we can now define functions in a way that depends only on the concept of set. Although this definition is not obviously related to the way we usually work with functions in mathematics, it is satisfying from a theoretical point of view, and computer scientists like it because it is particularly well suited for operating with functions on a computer. Definition A function F from a set A to a set B is a relation with domain A and co-domain B that satisfies the following two properties: 1. For every element x in A, there is an element y in B such that (x, y) E F. 2. For all elements x in A and y and z in B, if (x, y) E Fand (x, 2) E F, then y = z.
Transcribed Image Text:10:53 1 Functions In Section 1.2 we showed that ordered pairs can be defined in terms of sets and we defined Cartesian products in terms of ordered pairs. In this section we introduced relations as subsets of Cartesian products. Thus we can now define functions in a way that depends only on the concept of set. Although this definition is not obviously related to the way we usually work with functions in mathematics, it is satisfying from a theoretical point of view, and computer scientists like it because it is particularly well suited for operating with functions on a computer. Definition A function F from a set A to a set B is a relation with domain A and co-domain B that satisfies the following two properties: 1. For every element x in A, there is an element y in B such that (x, y) E F. 2. For all elements x in A and y and z in B, if (x, y) E Fand (x, 2) E F, then y = z.
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