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Exercise A

Avg difficulty 3.0

Using shortcuts, determine whether each sentence is a tautology, a contradiction, or neither.

  1. ¬B∧B\neg B\wedge B

  2. ¬D∨D\neg D\vee D

  3. (A∧B)∨(B∧A)(A\wedge B)\vee(B\wedge A)

  4. ¬[A→(B→A)]\neg[A\rightarrow(B\rightarrow A)]

  5. A↔[A→(B∧¬B)]A\leftrightarrow[A\rightarrow(B\wedge\neg B)]

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

  7. A→(B∨C)A\rightarrow(B\vee C)

  8. (A∧¬A)→(B∨C)(A\wedge\neg A)\rightarrow(B\vee C)

  9. (B∧D)↔[A↔(A∨C)](B\wedge D)\leftrightarrow[A\leftrightarrow(A\vee C)]

Magnus et al., forall x: Calgary, Truth tables, Truth table shortcuts, 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.