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Show that ifa is a subset of a universal setu, thena) A A

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 37E Chapter 2.2

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 37E

Show that ifa is a subset of a universal setu, thena) A ? A = ?.________________b) A ? ? = A.________________c) ________________d)

Step-by-Step Solution:
Step 1 of 3

Solution:Step1We have to show that if a is a subset of a universal set u. Step2a) A A = .L.H.S(left hand side)=R.H.S(right hand side)=Let x be an arbitrary element .L.H.S= = = = = ( As = = = R.H.SSo, A A = Step3b) A = A.L.H.S(left hand side)=R.H.S(right hand side)=ALet x be an arbitrary element .L.H.S=A = = = = ( where u is an universal set) = = A (As per identity law = R.H.SSo, A = A.Step4c. L.H.S(left hand side)=R.H.S(right hand side)=Let x be an arbitrary element .L.H.S= = = = = ( where u is an universal set) = (As = R.H.SSo, .Step5d. L.H.S(left hand side)=R.H.S(right hand side)=uLet x be an arbitrary element .L.H.S= = = = = ( where u is an universal set) = = R.H.SSo,

Step 2 of 3

Chapter 2.2, Problem 37E is Solved
Step 3 of 3

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Show that ifa is a subset of a universal setu, thena) A A