Counting false entries in truth tables of bracketed formulae connected by implication

Details Counting false entries in truth tables of bracketed formulae connected by implication Counting false entries in truth tables of bracketed formulae connected by implication

2011-06-22

arxiv.org/abs/1106.4443v1

Mathematics

Combinatorics

Scientific paper

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}.

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