there must be 9 combinations of booleans [closed]

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dont know if this is the correct stack exchange forum but i have the following puzzle

i have two booleans and they have 4 possible combinations

   X X
   X 0
   0 X
   0 0

2x2 = 4 , i thought

now i have three booleans, and i have those possible combinations

   X X X
   X X 0
   X 0 0
   0 0 0
   0 X X
   0 0 X
   X 0 X
   0 X 0

But there are only 8, i´m mentaly not able to find out the nineth combination, is there one ?

please Help me im stuck and always thought 3x3 = 9

Answer 1

You found all combinations. For each boolean you have 2 options. Combining 3 booleans you have 2 to the third power combinations, which equals 8.

So there is not a nineth combination.

This principle of combining options is the http://en.wikipedia.org/wiki/Rule_of_product

Answer 2

Your math is wrong. it's 2 ^ 3, not 3 * 3

2 ^ 3 = 2 * 2 * 2 = 8