Logic as a tool a guide to formal logical reasoning ( PDFDrive ) 306

k

(d)

[p]1

[¬(p ∨ ¬p)]3 p ∨ ¬p

⊥

¬p 1

[¬p]2 [¬(p ∨ ¬p)]3 p ∨ ¬p

⊥

¬¬p 2

⊥

p ∨ ¬p 3

(f) ND (( p → q ) ∧ ( p → ¬ q )) → ¬ p :

[p]1

[(p → q) ∧ (p → ¬q)]2

p → q q

[p]1

[(p → q) ∧ (p → ¬q)]2

p → ¬q

¬q

⊥

¬p 1 ((p → q) ∧ (p → ¬q)) → ¬p 2

[A]1

⊥

¬A 1

Hence ¬ B ND¬ A (b) Suppose ¬ B ND¬ A

[¬B]1

⊥

B 1

Hence A NDB