Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.03784 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909307321188352 |
|---|---|
| author | Freedman, Roy S. |
| author_facet | Freedman, Roy S. |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03784 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | N-Way Joint Mutual Exclusion Does Not Imply Any Pairwise Mutual Exclusion for Propositions Freedman, Roy S. Discrete Mathematics 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. |
| title | N-Way Joint Mutual Exclusion Does Not Imply Any Pairwise Mutual Exclusion for Propositions |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/2409.03784 |