For a selection of them, we then will prove the soundness of the resulting inference rule by deriving it in ND.. b Denote “Nina will go to a party” byp, and “Nina will go to office” byq.
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Answers and Solutions to Selected Exercises 285
2.4.6 (a)
[¬p]1, [¬p → r]3
⊥ 1
p p → ¬q [p]2 p → ¬q
¬q
(¬p → r) → ¬q 3
2
2.4.7 We formalize each of the propositional arguments by identifying the atomic propo-sitions in them and replacing them with propositional variables For a selection of them, we then will prove the soundness of the resulting inference rule by deriving
it in ND.
(b) Denote
“Nina will go to a party” byp, and
“Nina will go to office” byq Then the argument becomes:
p ∨ ¬ q, ¬ p ∨ ¬ q
The rule is derivable in ND and therefore sound, so the argument is correct.
[¬ q]2
¬ q
¬ q ∨ ¬ p[¬ q]1
¬ q
[¬ p]1,[p]2
⊥
¬ q
(d) Denote
“Socrates is happy” byp,
“Socrates is stupid” byq, and
“Socrates is a philosopher” byr Then the inference rule on which the argument is based is:
p ∨ ¬ q, p → ¬ r
r → ¬ q .
The rule is derivable in ND and therefore sound, so the argument is correct.
p ∨ ¬ q
[p]1, p → ¬ r
⊥
¬ q
[¬ q]1
¬ q
¬ q
r → ¬ q2
1