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Lets observe the parity property of integers while adding them or multiplying. It's simple to notice that when we add two numbers, the parity of the result depends on parity of summands:

x   y   x+y ----------- E   E    E E   O    O O   E    O O   O    E 

(Here "E" stands for "even", and "O" for "odd"). There is an obvious similarity with logical XOR function (when oddness is taken as True).

Ox  Oy    Ox xor Oy ------------------- F   F        F T   F        T F   T        T T   T        F 

(Ox and Oy means "oddness of x" and "... of y" resp.)

And the same thing is with multiplication, as it behaves like logical conjunction (AND).


And now the question is: why?
Thanks in advance :)

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    This fact was noticed by George Boole, about a century and a half ago: suitable logical operators behave somewhat like the familiar addition and multiplication. Since then, the area called Boolean Algebra has grown tremendously, with many applications. Congratulations on noticing the phenomenon.2012-09-24
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    So it's all up to strong relation between logical operations and arithmetic ones? (Assuming the former as a somewhat basis of latter)2012-09-24
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    Well, it may be more that one uses logical operators that have a strong analogy to arithmetic ones. For example, all of propsitional logic could be founded on a couple of operators, like implication and something else, that had no clear analogue in ordinary "algebra." So maybe it is that we have a preference for familiar patterns, and choose those (if possible) to analyze new stuff.2012-09-25

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