Discrete Mathematics with Applications 4th Edition

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

Chapter 6 - Set Theory - Exercise Set 6.1 - Page 351: 34

Answer

A1 = {1, 2, 3} A2 = {u, v} A3 = {m,n} a. A1 x (A2 x A3) = {1, 2, 3} x {(u, m), (u, n), (v, m), (v, n)} = {(1, (u, m)), (1, (u, n)), (1, (v, m)), (1, (v, n)), (2, (u, m)), (2, (u, n)), (2, (v, m)), (2, (v, n)), (3, (u, m)), (3, (u, n)), (3, (v, m)), (3, (v, n))} b. (A1 x A2) x A3 = {(1, u), (1, v), (2, u), (2, v), (3, u), (3, v)} x {m, n} = {((1, u), m), ((1, u), n), ((1, v), m), ((1, v), n), ((2, u), m), ((2, u), n), ((2, v), m), ((2, v), n), ((3, u), m), ((3, u), n), ((3, u), m), ((3, u), n)} c. A1 x A2 x A3 = {1, 2, 3} x {u, v} x {m, n} = {(1, u, m), (1, u, n), (1, v, m), (1, v, n), (2, u, m), (2, u, n), (2, v, m), (2, v, n), (3, u, m), (3, u, n), (3, v, m), (3, v, n)}

Work Step by Step

A1 = {1, 2, 3} A2 = {u, v} A3 = {m,n} a. A1 x (A2 x A3) = {1, 2, 3} x {(u, m), (u, n), (v, m), (v, n)} = {(1, (u, m)), (1, (u, n)), (1, (v, m)), (1, (v, n)), (2, (u, m)), (2, (u, n)), (2, (v, m)), (2, (v, n)), (3, (u, m)), (3, (u, n)), (3, (v, m)), (3, (v, n))} b. (A1 x A2) x A3 = {(1, u), (1, v), (2, u), (2, v), (3, u), (3, v)} x {m, n} = {((1, u), m), ((1, u), n), ((1, v), m), ((1, v), n), ((2, u), m), ((2, u), n), ((2, v), m), ((2, v), n), ((3, u), m), ((3, u), n), ((3, u), m), ((3, u), n)} c. A1 x A2 x A3 = {1, 2, 3} x {u, v} x {m, n} = {(1, u, m), (1, u, n), (1, v, m), (1, v, n), (2, u, m), (2, u, n), (2, v, m), (2, v, n), (3, u, m), (3, u, n), (3, v, m), (3, v, n)}
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