Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 1 - Speaking Mathematically - Exercise Set 1.2: 11

Answer

a. $A\times B=\{(w,a), (w,b), (x,a), (x,b), (y,a), (y,b), (z,a), (z,b)\}$. This set contains 8 elements. b. $B\times A=\{(a,w), (a,x), (a,y), (a,z), (b,w), (b,x), (b,y), (b,z)\}$. This set contains 8 elements. c. $A\times A=\{(w,w), (w,x), (w,y), (w,z), (x,w), (x,x), (x,y), (x,z), (y,w), (y,x), (y,y), (y,z), (z,w), (z,x), (z,y), (z,z)\}$. This set contains 16 elements. d. $B\times B=\{(a,a), (a,b), (b,a), (b,b)\}$. This set contains 4 elements.

Work Step by Step

The number of elements in a Cartesian product is equal to the product of the number of elements in each set. Note that the order of the elements in the Cartesian product is irrelevant, but the order of the elements in the ordered pairs within the Cartesian product is relevant (e.g., $(1,2)\ne(2,1)$).
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