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arXiv · 2409.03784

N-Way Joint Mutual Exclusion Does Not Imply Any Pairwise Mutual Exclusion for Propositions

Roy S. Freedman
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Abstract

Given a set of N propositions, if any pair is mutual exclusive, then the set of all propositions are N-way jointly mutually exclusive. This paper provides a new general counterexample to the converse. We prove that for any set of N propositional variables, there exist N propositions such that their N-way conjunction is zero, yet all k-way component conjunctions are non-zero. The consequence is that N-way joint mutual exclusion does not imply any pairwise mutual exclusion. A similar result is true for sets since propositional calculus and set theory are models for two-element Boolean algebra.

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Roy S. Freedman. 2024-08-29. N-Way Joint Mutual Exclusion Does Not Imply Any Pairwise Mutual Exclusion for Propositions. https://arxiv.org/abs/2409.03784

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