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: 28

Answer

$yes\,\,,\left \{ E,O \right \}\,is\,a\,partition\,\,of\,\,\mathbb{Z}.$ $E\,\,be\,\,the\,\,set\,\,of\,\,all\,\,even\,\,integers\,\,,\,\,O\,\,the\,\,set\,\,of\,\,all\,\,odd\,\, integers\,\,and\,\,\mathbb{Z}\,the\,set\,of\,\,all\,\,integers$

Work Step by Step

$E\,\,be\,\,the\,\,set\,\,of\,\,all\,\,even\,\,integers\,\,,\,\,O\,\,the\,\,set\,\,of\,\,all\,\,odd\,\, integers\,\,and\,\,\mathbb{Z}\,the\,set\,of\,\,all\,\,integers$ $E=\left \{ 0,2,4,6,.... \right \}\,\,,O=\left \{ 1,3,5,7,.... \right \} $ $E\cup O=\mathbb{Z} (as\,\,every\,\,integer\,\,either\,\,odd\,\,or\,\,even\,)$ $\,\,and\,\,E\cap O=\varnothing \,\,(as\,any\,integer\,\,can\,\,not\,\,be\,both\,odd\,and\,even)$ $so \left \{ E,O \right \}\,is\,a\,partition\,\,of\,\,\mathbb{Z}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.