1. A ⊃ (B • C)
2. ∼D ⊃ ∼B
3. A / D
-Which of the following propositions is a likely last line of the indented sequence for an indirect proof of the given argument?
A) A • ∼A
B) B • ∼B
C) C • ∼C
D) All three options above are equally likely

Question

Quizplus · Accepted Answer

To prove the argument indirectly, we assume ∼(B•C) (the negation of the consequent). Combining with the first premise, we get ∼A. From the second premise, we can infer ∼∼B, which is equivalent to B. Since we derived both ∼A and B, we can conclude that A and ∼B together imply a contradiction. Therefore, the last line should be B•∼B (not A•∼A or C•∼C, which are irrelevant to the argument).

1. a ⊃ (B • C)