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Cartesian Product of Two Sets A and B

publish date: 2022/07/14 01:53:00 GMT+10

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Let A = {1, 2, 3} and B = {5, 6}, what is the cartesian products of these two sets?

A × B = ?

{(1, 5), (2, 5), (3, 5), (1, 6), (2, 6)}

{(1, 5), (2, 5), (3, 5), (1, 6), (3, 6)}

{(1, 5), (2, 5), (3, 5), (2, 6), (3, 6)}

{(1, 5), (2, 5), (3, 5), (1, 6), (2, 6), (3, 6)}

{(1, 5), (2, 5), (3, 5), (1, 6), (2, 6), (3, 6)}

We define the Cartesian product of A and B, written A × B, to be the set of all ordered pairs (x, y) where x ∈ A and y ∉ B. Thus,

A × B = {(x, y)|x ∈ A and y ∈ B}

{(1, 5), (2, 5), (3, 5), (1, 6), (2, 6), (3, 6)} is the set the satisfy all cartesian products of all the elements of both sets A and B

Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012, go-math-science.com