Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 2 - Section 2.1 - Sets - Exercises - Page 126: 35

Answer

$mn$

Work Step by Step

$Proof.$ Let $A$ and $B$ be sets, suppose $A$ has $m$ elements, and suppose $B$ has $n$ elements. We know $A \times B$ is a set of ordered pairs, where the first coordinate of each ordered pair comes from $A$, the second coordinate of each ordered pair comes from $B$, and each element of $A$ is paired with each element of $B$. So each of the $m$ elements in $A$ appears as the first coordinate in $n$ ordered pairs. Hence there are $mn$ distinct ordered pairs in $A \times B._\Box$
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