# The output of a Boolean function is 0 or 1

*label*Programming

*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?