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Exercise C

Avg difficulty 3.0

Use complete or partial truth tables (as appropriate) to determine whether each argument is valid or invalid:

  1. A∨[A→(A↔A)]∴AA\vee\bigl[A\rightarrow(A\leftrightarrow A)\bigr]\therefore A

  2. A↔¬(B↔A)∴AA\leftrightarrow\neg(B\leftrightarrow A)\therefore A

  3. A→B,B∴AA\rightarrow B,B\therefore A

  4. A∨B,B∨C,¬B∴A∧CA\vee B,B\vee C,\neg B\therefore A\wedge C

  5. A↔B,B↔C∴A↔CA\leftrightarrow B,B\leftrightarrow C\therefore A\leftrightarrow C

Magnus et al., forall x: Calgary, Truth tables, Partial truth tables, Exercise C

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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.