(A'B' + AB)(A'B + AB')(A + B)

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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(A'B' + AB)(A'B + AB')(A + B)

Expert Solution
Step 1

Let's simplify the given expression using Boolean algebra:-

 

First, we can apply the distributive law to the first two terms:

 

(A'B' + AB)(A'B + AB')(A + B)
= (A'B'A' + A'BA)(A'B + AB') (A + B)        // distribute A'B' over AB
= (A'A'B'B + A'BA'B + A'B'A' + ABA)(A + B') (A + B) // distribute A'B over AB'
= (0 + A'BA'B + A'B'A' + ABA)(A + B') (A + B) // A'A'B'B = 0 using A'A = 0 and B'B = 0
= (A'BA'B + A'B'A' + ABA)(A + B') (A + B)      // identity law: 0 + X = X

 

Next, we can apply the distributive law again:

(A'BA'B + A'B'A' + ABA)(A + B') (A + B)
= (A'BA'B)(A + B') (A + B) + (A'B'A')(A + B') (A + B) + (ABA)(A + B') (A + B) // distribute over (A + B') and (A + B)
= (A'BA'BA + A'BA'BB' + ABA'A + ABA'B' + A'B'BA + A'B'BB' + ABA'A + ABA'B')(A + B)  // distribute over (A + B)

 
 

 

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