SOLUTION: Use natural deduction to derive the conclusion of the following arguments. Do not use conditional proof or indirect proof. 1. (D & E) ⊃ (F & G) 2. (~E v ~ D) ⊃ (H •

Algebra ->  Conjunction -> SOLUTION: Use natural deduction to derive the conclusion of the following arguments. Do not use conditional proof or indirect proof. 1. (D & E) ⊃ (F & G) 2. (~E v ~ D) ⊃ (H •      Log On


   

Question 1132212: Use natural deduction to derive the conclusion of the following arguments. Do not use conditional proof or indirect proof.
1. (D & E) ⊃ (F & G)
2. (~E v ~ D) ⊃ (H • I )
3. ~F
Conclusion: I
Answer by solver91311(24713) About Me  (Show Source):
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1.  (D & E) -> (F & G)
2.  (~E V ~D) -> (H & I)
3.  ~F                     |  I

4. ~F V ~G                 3.  Disjuction Introduction
5. ~(F & G)                4.  DeMorgan
6. ~(D & E)                1.  Modus Tollens
7. ~E V ~D                 6.  DeMorgan
8.  H & I                  2.  Modus Ponens
9.  Therefore I            8.  Conjunction Elimination


Note Disjunction Introduction is also called Addition. Conjunction Elimination is also called Simplification.


John

My calculator said it, I believe it, that settles it