SOLUTION: Use conditional proof: 1. N ⊃ (F • A) 2. B ⊃ (R • F) / (N ∨ B) ⊃ (A ∨ R)

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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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