The output of a Boolean function is 0 or 1

timer Asked: Sep 24th, 2013

Question description

The output of a Boolean function is 0 or 1. Interpret these as numbers, so 0 < 1. A Boolean function is called non-decreasing if f(x) >= f(y) for two domain elements (x, y) in x^n {0,1} whenever "the number of 1's in x" is greater than or equal to "the number of 1's in y".
How many non-decreasing functions of 2 and 3 Boolean variables exist?
How many non-decreasing functions of n Boolean variables exist?

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