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.
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