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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.03784 |
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Table of Contents:
- 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.