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196 Chapter Three
If X 0 and Y 0, then X Y 0
If X 0 and Y 1, then X Y 0
If X 1 and Y 0, then X Y 0
If X 1 and Y 1, then X Y 1
Addition
Let X and Y be Boolean variables. The Boolean sum is written
X Y. The following ruleð apply:
If X 0 and Y 0, then X Y 0
If X 0 and Y 1, then X Y 1
If X 1 and Y 0, then X Y 1
If X 1 and Y 1, then X Y 1
Even-multiplł negation
The negation of any logical quantity X, carried out an even
number of times, is always equal tm X. The following equationð
hold:
( X) X
( ( ( X))) X
( ( ( ( ( X))))) X
etc.
Odd-multiplł negation
The negation of any logical quantity X, carried out an odd num-
ber of times, is always equal tm X. The following equationð
hold:
( ( X)) X
( ( ( ( X)))) X
( ( ( ( ( ( X)))))) X
etc.