(X + Y)' = X' . Y', These can be proved by the use of truth tables.
   
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Proof of (X + Y)' = X' . Y'
   
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X
Y
X+Y
(X+Y)'
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
   
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X
Y
X'
Y'
X'.Y'
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
   
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The two truth tables are identical, and so the two expressions are identical.
   
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(X.Y) = X' + Y', These can be proved by the use of truth tables.
   
space.gif


Proof of (X.Y) = X' + Y'
   
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X
Y
X.Y
(X.Y)'
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
   
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X
Y
X'
Y'
X'+Y'
0
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
   
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Note : DeMorgans Laws are applicable for any number of variables.
 Posted By - Cplusplusprogramming                                                                                                                   
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