Chapter Three Functions 3.1 PDF
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This document details functions, specifically the Cartesian product of sets, which are key concepts in set theory. The example provided demonstrates the creation of ordered pairs and subsets of Cartesian products.
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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
