Question 881255: Premise 1: D⊃ [D⊃ (B & ~Q)]
Premise 2: (~Q & B)⊃ C
Conclusion: D⊃ C
Direct Deduction
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Basic idea
Step 1) Assume D is true
Step 2) If D is true, then D⊃ (B & ~Q) is true (Modus Ponens, Premise 1)
Step 3) if D⊃ (B & ~Q) is true, and D is true, then B & ~Q is true (Modus Ponens again)
Step 4) B & ~Q is the same as ~Q & B (commutation)
Step 5) If ~Q & B is true, then C is true (Modus Ponens, Premise 2)
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So assuming D is true leads to C being true. That leads to the conclusion D⊃ C
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