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Exercise 8

Avg difficulty 2.5

Simplify the following statements (so that negation only appears right before variables).

  1. ¬(P→¬Q)\neg(P \imp \neg Q).
  2. (¬P∨¬Q)→¬(¬Q∧R)(\neg P \vee \neg Q) \imp \neg (\neg Q \wedge R).
  3. ¬((P→¬Q)∨¬(R∧¬R))\neg((P \imp \neg Q) \vee \neg (R \wedge \neg R)).

  4. It is false that if Sam is not a man then Chris is a woman, and that Chris is not a woman.

Levin, Discrete Mathematics: An Open Introduction (3rd ed.), §4.1 Propositional Logic, Exercise 8

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Adapted from Discrete Mathematics: An Open Introduction © 2013–2019 Oscar Levin. Licensed under CC BY-SA 4.0. Source: Discrete Mathematics: An Open Introduction. Imported at revision 1e2e26b.