Chapter Three Functions PDF
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Summary
This document or chapter discusses functions and relations between sets based on ordered pairs. It provides definitions and examples related to Cartesian products and relations within a mathematics context.
Full Transcript
Chapter Three Functions 3.1 Definition 3.1.1 Suppose A and B are sets. The Cartesian product of A and B , denoted by A × B is the set which contains every ordered pair whose first coordinate is an element of A and second coordinate is an element of B , i.e. A × B = {(a, b) : a...
Chapter Three Functions 3.1 Definition 3.1.1 Suppose A and B are sets. The Cartesian product of A and B , denoted by A × B is the set which contains every ordered pair whose first coordinate is an element of A and second coordinate is an element of B , i.e. A × B = {(a, b) : a ∈ A and b ∈ B} Example 3.1.1 For A = {2, 4} and B = {−1, 3} , we have a) A × B = {(2, −1), (2, 3), (4, −1), (4, 3)} and b) B × A = {(−1, 2), (−1, 4), (3, 2), (3, 4)} Definition 3.1.2 If A and B are sets, any subset of A × B is called a relation from A into B. () March 21, 2023 2/2
