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Exercise A

Avg difficulty 3.0

Consider the following sentences:

  1. (A→¬B)(A\rightarrow\neg B)

  2. ¬(A↔B)\neg(A\leftrightarrow B)

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

  4. (¬(A→B)∧(A→C))(\neg(A\rightarrow B)\wedge(A\rightarrow C))

  5. (¬(A∨B)↔((¬C∧¬A)→¬B))(\neg(A\vee B)\leftrightarrow((\neg C\wedge\neg A)\rightarrow\neg B))

  6. ((¬(A∧¬B)→C)∧¬(A∧D))((\neg(A\wedge\neg B)\rightarrow C)\wedge\neg(A\wedge D))

For each sentence, find an equivalent sentence in DNF and one in CNF.

Magnus et al., forall x: Calgary, Metatheory, Normal forms, 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.