(a) Give the reasons for the steps given to validate the argument
[(p → q) ∧ (¬r ∨ s) ∧ (p ∨ r)] → (¬q → s).
Steps Reasons
(1) ¬ (¬q → s)
(2) ¬q ∧ ¬s
(3) ¬s
(4) ¬r ∨ s
(5) ¬ r
(6) p → q
(7) ¬ q
(8) ¬ p
(9) p ∨ r
(10) r
(11) ¬ r ∧ r
(12) ∴ ¬q → s
(b) Give a direct proof for the result in part (a).
(c) Give a direct proof for the result in Example 2.32