SOLUTION: ~b → ~r e → (f → y) ~(e → y) f V (m V r) ___________ m V b

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Question 1061555: ~b → ~r
e → (f → y)
~(e → y)
f V (m V r)
____________
m V b
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
I used to be very, very, good at these when I was in my sophomore year of engineering school (1984). I'm trying to re-educate myself in formal logic so I can be helpful.
& = AND
—
1. ~b —> ~r
2. e —> (f —> y)
3. ~(e —> y)
4. f V (m V r)
—
// start proof here
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5. ~(~e V y)           (3, Impl = material implication)        
6. ~~e & ~y           (5, DM= DeMorgan's)
7.  ~y                   (6, Simp = Simplification)
8.  ~~e                 (6, Simp)
9.  e                     (8, DN = double negative)
10.  f—>y             (9,2  MP = Modus Ponens)
11.  ~f                  (10,7 MT = Modus Tollens, same as contrapositive)
12.  m V r             (10,4 MTP = Modus Tollendo Ponens "affirm by denying")
+13. r                  Conditional (aim is to show if r is true, then b must be true)
| 14.  ~~r              (13, DN)
| 15. ~~b              (14, 1  MT)
| 16.  b                 (15, DN) 
>14. r—>b           Ends Conditional Proof 
 15.  m V b            (12,14 Substitution)   Conclusion   
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