SOLUTION: Premise 1: D⊃ [D⊃ (B & ~Q)] Premise 2: (~Q & B)⊃ C Conclusion: D⊃ C Direct Deduction

Algebra.Com
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)

-------------------------------------------------------

So assuming D is true leads to C being true. That leads to the conclusion D⊃ C

RELATED QUESTIONS

Use natural deduction to derive the conclusion of the following arguments. Do not use... (answered by math_helper)
Please help! A ⊃ B A ⊃ (B ⊃ C) B ⊃ (C ⊃ D) ∴ A... (answered by Edwin McCravy)
Please help me solve this proof! Premises: 1. (A⊃B)&(C⊃D) 2.... (answered by Edwin McCravy)
Premises: 1. A ⊃ X 2. X ⊃ (B... (answered by math_helper)
∼A∙~B ~D⊃A M⊃[(NvO)⊃P] Q⊃(SvT)... (answered by jim_thompson5910)
Using a conditional proof: 1. (D v E) ⊃ (F · G) 2.( A v B) ⊃ (D · C) (answered by jim_thompson5910)
Could you please help me? Im sick with a bug and cant think straight :/ A) 1. A ⊃ (answered by solver91311)
I need help solving this proof, please help! Premises: 1. A ⊃ (B⊃C) 2. A & (answered by Edwin McCravy)
Does this proof look correct to you? If you notice any mistakes please let me know! Thank (answered by jim_thompson5910)