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Exercise H

Avg difficulty 3.0

Determine whether each collection of sentences is jointly satisfiable or jointly unsatisfiable, using a complete truth table.

  1. ¬B\neg B, A→BA\rightarrow B, AA

  2. ¬(A∨B)\neg(A\vee B), A↔BA\leftrightarrow B, B→AB\rightarrow A

  3. A∨BA\vee B, ¬B\neg B, ¬B→¬A\neg B\rightarrow\neg A

  4. A↔BA\leftrightarrow B, ¬B∨¬A\neg B\vee\neg A, A→BA\rightarrow B

  5. (A∨B)∨C(A\vee B)\vee C, ¬A∨¬B\neg A\vee\neg B, ¬C∨¬B\neg C\vee\neg B

Magnus et al., forall x: Calgary, Truth tables, Semantic concepts, Exercise H

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Adapted from forall x: Calgary © 2025 P. D. Magnus, Tim Button, Robert Trueman, and Richard Zach. Licensed under CC BY 4.0. Source: forall x: Calgary. Imported at revision ec34df8.