SOLUTION: If you could help me to figure out this problem I would really appreciate it. I've tried implication, transitivity and i still can't seem to get it. 1.C>A 2.B>C solution:(CvB)

Algebra ->  Proofs -> SOLUTION: If you could help me to figure out this problem I would really appreciate it. I've tried implication, transitivity and i still can't seem to get it. 1.C>A 2.B>C solution:(CvB)      Log On


   

Question 199524: If you could help me to figure out this problem I would really appreciate it. I've tried implication, transitivity and i still can't seem to get it.
1.C>A
2.B>C solution:(CvB)>A
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: * means "and" 

1.   C -> A 
2.   B -> C    :. (C v B) -> A
-------------------------------
3.   B -> A                        2,1     Hypothetical Syllogism 
4.   ~B v A                          3     Material Implication
5.   A v ~B                          4     Commutation
6.   ~C v A                          1     Material Implication
7.   A v ~C                          6     Commutation
8.   (A v ~C) * (A v ~B)           7,5     Conjunction
9.   A v (~C * ~B)                   8     Distribution
10.  (~C * ~B) v A                   9     Commutation  
11.  ~(C v B) v A                   10     De Morgan's Theorem 
12.  (C v B) -> A                   11     Material Implication