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 6.3 - Page 373: 49

Answer

$A\bigtriangleup A^c = (A - A^c) \cup (A^c - A) \\ =(A \cap (A^c)^c) \cup (A^c \cap A^c) \\ (set\,\,dif\! ference\,\,law )\\ =(A\cap A)\cup (A^c \cap A^c)\\ (double\,\,complement\,\,law)\\ =A\cup A^c\\ by(idempotent\,\,law)\\ =U \\ (complement\,\,law\,\,for\,\cup ) $

Work Step by Step

$A\bigtriangleup A^c = (A - A^c) \cup (A^c - A) \\ =(A \cap (A^c)^c) \cup (A^c \cap A^c) \\ (set\,\,dif\! ference\,\,law )\\ =(A\cap A)\cup (A^c \cap A^c)\\ (double\,\,complement\,\,law)\\ =A\cup A^c\\ by(idempotent\,\,law)\\ =U \\ (complement\,\,law\,\,for\,\cup ) $
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