PHILOSOPHY Prove the validity of the following abstract arguments:

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Ch. 3–6 Using only MP, MT, DN, Simp, Conj, CS, DS, Disj, and DM.

Prove the validity of the following abstract arguments:

a)

  1. ¬(S ∨ T) Prem
  2. A → (S ∨ T) Prem
  3. P ∨ A Prem
  4. ¬Q ∨ A Prem /∴ P & ¬Q

b)

  1. ¬B & ¬C Prem
  2. ¬C → D Prem
  3. (D & ¬B) → (E → ¬H) Prem
  4. E & (F → H) Prem /∴ ¬F

c)

  1. (C → F) & G Prem
  2. (F → D) ∨ D Prem
  3. ¬D Prem /∴ ¬C ∨ H

d)

  1. H → ¬(K & J) Prem
  2. ¬(¬K ∨ D) Prem
  3. ¬¬H Prem /∴ ¬J