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: 48

Answer

$A\bigtriangleup \varnothing = (A - \varnothing ) \cup (\varnothing - A) \\ =(A \cap \varnothing^c ) \cup (\varnothing \cap A^c) \\ (set\,\,dif\! ference\,\,law )\\ =(A \cap U ) \cup (\varnothing \cap A^c) \\ (complement\,\,law\,for\,\varnothing) \\ =A\cup (\varnothing \cap A^c)\\ (identity\,law\,for\,\cap )\\ =A\cup \varnothing \\ (def.of\varnothing )\\ =A $

Work Step by Step

$A\bigtriangleup \varnothing = (A - \varnothing ) \cup (\varnothing - A) \\ =(A \cap \varnothing^c ) \cup (\varnothing \cap A^c) \\ (set\,\,dif\! ference\,\,law )\\ =(A \cap U ) \cup (\varnothing \cap A^c) \\ (complement\,\,law\,for\,\varnothing) \\ =A\cup (\varnothing \cap A^c)\\ (identity\,law\,for\,\cap )\\ =A\cup \varnothing \\ (def.of\varnothing )\\ =A $
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