Question 1139588: Use conditional proof:
1. N ⊃ (F • A)
2. B ⊃ (R • F) / (N ∨ B) ⊃ (A ∨ R)
Found 2 solutions by Edwin McCravy, jim_thompson5910:
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! Use conditional proof:
1. N ⊃ (F • A)
2. B ⊃ (R • F) / (N ∨ B) ⊃ (A ∨ R)
3. | N v B ACP
4. | (F • A) v (R • F) 1,2,3, Constructive Dilemma
5. | (F • A) v (F • R) 4, Commutation
6. | F • (A v R) 5, Distribution
7. | (A v R) • F 6, Commutation
8. | A v R 7, Simplification
9. (N ∨ B) ⊃ (A ∨ R) lines 3-8 conditional proof
Edwin
Answer by jim_thompson5910(35256)  (Show Source):
You can put this solution on YOUR website!
In place of the horseshoe symbol, I will use an arrow. Also, instead of a dot symbol, I will use an ampersand. For me it's easier to use these symbols for the spreadsheet diagram below.
The idea is to assume the antecedent N v B and show that it leads to A v R
The assumption is made on line 3. From there you use the logic rules of inference/replacement until you arrive at line 9. Lines 3 through 9 all combine to end up with the proper conclusion we want to derive.
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