Almost every 2-SAT function is unate

Bollob´as, Brightwell and Leader showed that there are at most 2^(n 2)+o(n2) 2-SAT functions on n variables, and conjectured that in fact the number of 2-SAT functions on n variables is 2^(n 2)+n(1 + o(1)). We prove their conjecture. As a corollary of this, we also find the expected number of satisfying assignments of a random 2-SAT function on n variables. We also find the next largest class of 2-SAT functions and show that if k = k(n) is any function with k(n) < n1/4 for all sufficiently large n, then the class of 2-SAT functions on n variables which cannot be made unate by removing 25k variables is smaller than 2(n 2)+n−kn for all sufficiently large n.