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 :)