Inconsistent triad

An inconsistent triad is a set of three propositions that cannot all be true together. For example, 'She was an orphan; Tim outlived her; Tim was her father'.^[1]

All inconsistent triads lead to trilemmas:

If A and B are true, C must be false.
If A and C are true, B must be false.
If B and C are true, A must be false.^[2]

^ "The Oxford companion to philosophy". Choice Reviews Online. 33 (5): 33–2495–33-2495. 1996-01-01. doi:10.5860/CHOICE.33-2495 (inactive 22 February 2025). S2CID 142841293.{{cite journal}}: CS1 maint: DOI inactive as of February 2025 (link)
^ Sullivan, Scott M. (2005-10-26). An Introduction To Traditional Logic: Classical Reasoning For Contemporary. Booksurge Publishing. ISBN 978-1-4196-1671-6.

[1] "The Oxford companion to philosophy". Choice Reviews Online. 33 (5): 33–2495–33-2495. 1996-01-01. doi:10.5860/CHOICE.33-2495 (inactive 22 February 2025). S2CID 142841293.{{cite journal}}: CS1 maint: DOI inactive as of February 2025 (link)

[2] Sullivan, Scott M. (2005-10-26). An Introduction To Traditional Logic: Classical Reasoning For Contemporary. Booksurge Publishing. ISBN 978-1-4196-1671-6.

[1]

[2]