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Back to Semantic concepts

Exercise A

Avg difficulty 3.0

Revisit your answers to exercise 3A. Determine which sentences were tautologies, which were contradictions, and which were neither tautologies nor contradictions.

  1. A→AA\rightarrow A

  2. C→¬CC\rightarrow\neg C

  3. (A↔B)↔¬(A↔¬B)(A\leftrightarrow B)\leftrightarrow\neg(A\leftrightarrow\neg B)

  4. (A→B)∨(B→A)(A\rightarrow B)\vee(B\rightarrow A)

  5. (A∧B)→(B∨A)(A\wedge B)\rightarrow(B\vee A)

  6. ¬(A∨B)↔(¬A∧¬B)\neg(A\vee B)\leftrightarrow(\neg A\wedge\neg B)

  7. [(A∧B)∧¬(A∧B)]∧C\bigl[(A\wedge B)\wedge\neg(A\wedge B)\bigr]\wedge C

  8. [(A∧B)∧C]→B[(A\wedge B)\wedge C]\rightarrow B

  9. ¬[(C∨A)∨B]\neg\bigl[(C\vee A)\vee B\bigr]

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

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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.