For every element r in A, there is an element y in B such that (x, y) is in F. Can you explain how does this differ from a relation? Please answer this in a couple sentences NO NEED TO SHOW PROOF! AGAIN NO PROOF PLEASE!!!

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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For every element r in A, there is an element y in B such that (x, y) is in F. Can you explain how does this differ from a relation? Please answer this in a couple sentences NO NEED TO SHOW PROOF! AGAIN NO PROOF PLEASE!!!
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.
Transcribed Image Text: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.
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