Homework #3 SolutionsPhilosophy 12AMarch 8, 2010Part One1.A→CB→CA∨B∴Cis avalidargument. There are no rows in which all of its premises are true and its conclusion is false:ABCA→CB→CA∨BC>>>>>>>>>⊥⊥⊥>⊥>⊥>>>>>>⊥⊥⊥>>⊥⊥>>>>>>⊥>⊥>⊥>⊥⊥⊥>>>⊥>⊥⊥⊥>>⊥⊥2.I→N(∼K∨D)↔ND→∼I∴∼I→(N→K)is aninvalid argument. Here’s a row that makes all its premises true and its conclusion false:DIKNI→N(∼K∨D)↔ND→∼I∼I→(N→K)>⊥⊥>>>>⊥3.(∼O→∼S)&(O→(M&∼I))∼I→∼M∴∼Sis avalidargument. For the conclusion ‘∼S’ to be false, we require ‘S’ to be true. Now,for the first premise of this argument to be true, its first conjunct ‘∼O→∼S’ must be true. Hence, the antecedent ‘∼O’of this first conjunct must be false (since its consequent ‘∼S’ has already been assumed to be false). So ‘O’ must betrue. But, if ‘O
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