 Minority Boolean function

For an odd number of input bits, this Boolean function is one exactly when fewer than half of the inputs are one. For three inputs, $m(a,b,c)=\neg a\neg b\vee \neg a\neg c\vee \neg b\neg c$. Each term says that a specified pair of inputs is zero; at most one input can then be one. This proves both directions of the formula.