Counting false entries in truth tables of bracketed formulae connected by implication
Combinatorics
2011-06-23 v1 Logic
Abstract
In this paper we count the number of rows f_n with the value "false" in the truth tables of all bracketed formulae with n distinct variables connected by the binary connective of implication. We find a recurrence and an asymptotic formulae for f_n. We also show that the ratio of f_n to the total number of rows converges to \frac{3-\sqrt{3}}{6}.
Cite
@article{arxiv.1106.4443,
title = {Counting false entries in truth tables of bracketed formulae connected by implication},
author = {Peter J. Cameron and Volkan Yildiz},
journal= {arXiv preprint arXiv:1106.4443},
year = {2011}
}