On the Number of 2-SAT Functions

We give an alternative proof of a conjecture of Bollob'as, Brightwell and Leader, first proved by Peter Allen, stating that the number of boolean functions definable by 2-SAT formulae is $(1+o(1))2^{\left(\genfrac{}{}{0px}{}{n+1}{2}\right)}$. One step in the proof determines the asymptotics of the number of “odd-blue-triangle-free” graphs on $n$ vertices.