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Find the complement of the below expression using Demorgan' s law    (x'y' + xy' + y(xy'))

Find the complement of the below expression using Demorgan' s law    (x'y' + xy' + y(xy'))

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Find the complement of the below expression using Demorgan' s law 

 

(x'y' + xy' + y(xy'))

Expert Solution
Step 1

Taking the complement of whole expression -

(x'y' + xy' + y(xy'))'

Applying De-morgan's Law, ( A + B )' = A'B'  

(x'y')' .(xy')'. (y(xy'))'

Applying De-morgan's Law,   ( AB)' = A' + B '

(x + y) . (x'+y) . (y'+(xy')')

Applying De-morgan's Law,   ( AB)' = A' + B '

(x + y) . (x'+y) .(y'+x' + y)

By applying Complement law (A+A'=1) ,

(x + y) . (x'+y) .(x'+1)

By multiplying (x+y ) to ( x' + y) ,

(xx' + x'y + xy + y)

  By using Complement law ( A.A'=0),

(x'y + xy + y)

now taking y as common part ,

(x'y +y(1 + x))

By applying Annulent law , ( A + 1 = A)

(x'y + y)

Taking y as common part ,

y( x' + 1)  = y 

 

 

 

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