3.4.x. Exercise questions

1.

The following arguments are not formally valid. In each case, use a derivation to show this and present a counterexample that the derivation leads you to.

  a. ¬ B / ¬ (A ∧ ¬ B)
  b. ¬ (A ∧ B) / ¬ A ∧ ¬ B
  c. ¬ (A ∧ B), ¬ (B ∧ C) / ¬ (A ∧ C)
2.

Use derivations to check the following claims of entailment. If the claim fails, present a counterexample that the derivation leads you to.

  a. ¬ (A ∧ ¬ B) ⇒ B
  b. ¬ (A ∧ B) ⇒ ¬ (B ∧ A)
  c. ¬ (A ∧ ¬ B) ⇒ ¬ (B ∧ ¬ A)
  d. ¬ (A ∧ B), ¬ (B ∧ C), B ⇒ ¬ A ∧ ¬ C
  e. ¬ (A ∧ ¬ (B ∧ ¬ (C ∧ ¬ D))) ⇒ ¬ (A ∧ ¬ (B ∧ D))

For more exercises, use the exercise machine.

Glen Helman 28 Aug 2008