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qid 11122 · philosophy

Question: Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.) (T ⊃ U) ⊃ (W ⊃ U) T ⊃ ~(U ⊃ X) (T ⊃ ~X) ⊃ W

  1. Inconsistent. Inconsistent valuation when T, U, W and X are all false
  2. Inconsistent. Inconsistent valuation when T, U, W and X are all true
  3. Consistent. Consistent valuation when T, U and X are true and W is false
  4. Consistent. Consistent valuation when U, W, and X are true and T is false
  5. Inconsistent

Our answer: D. Consistent. Consistent valuation when U, W, and X are true and T is false Source quote machine-checked (exact quote)

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Current source

Humanities LibreTexts, Thinking Well: A Logic and Critical Thinking Textbook (Lavin), 7.5 Logical Analysis Using Truth Tables

https://human.libretexts.org/Bookshelves/Philosophy/Logic_and_Reasoning/Thinking_Well_-_A_Logic_And_Critical_Thinking_Textbook_4e_(Lavin)/07%3A_Propositional_Logic/7.05%3A_Logical_Analysis_using_Truth_Tables

“A consistent set of propositions is one where the logical form or structure of those propositions allows them to all be true at the same time.”

Source quote machine-checked (exact quote)

retrieved 2026-09-18T01:17:53.230Z

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Earlier version (superseded)

https://en.wikipedia.org/wiki/Material_conditional

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retrieved 2026-09-17T09:30:25.477Z

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Earlier version (superseded)

No public source has been found for this card yet (2 places checked internally).

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