CSE370 Quiz 1 (6 October) Solution
 
 

Given the following Boolean function:
 

F1 = ABC + A'BC + A'B'C + A'BC' + A'B'C'


Show, using perfect induction (truth table) that it is equivalent to:
 

F2 = BC + A'B' + A'C'
A
B
C
ABC
A'BC
A'B'C
A'BC'
A'B'C'
F1
BC
A'B'
A'C'
F2
0
0
0
0
0
0
 0 
1
1
0 
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
 0
0
0
0
0
0
0
0
0
0
1
0
1
 0
0
0
0
0
0
0
0
0
0
1
1
0
 0
0
0
0
0
0
0
0
0
0
1
1
1
 1
0
0
0
0
1
1
0
0
1
The truth-table demonstrates that F1 and F2 are equivalent because they have the same value for ALL combinations of input values.


Show using the theorems of Boolean algebra that F2 is equivalent to (make sure to show each step of your work):
 

BC + A'B' + A'C'  = ABC + A'
(A + A')BC  + A'B'(C + C') + A'(B + B')C'
ABC + A'BC + A'B'C + A'B'C' + A'BC' + A'B'C'
ABC + A'BC + A'B'C + A'B'C' + A'BC'
ABC + A' (BC + BC' + B'C + B'C')
ABC + A' (B(C + C') + B'(C + C'))
ABC + A'(B + B')
ABC + A'
alternatively:
BC + A'B' + A'C'
BC + A'(B' + C')
BC + A'(BC)'
BC + A'
ABC + A'

 
 
 
 
 
 
 
 
 
 
 
 
 

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