SOLUTION: If you could help me with the problem I would really appreciate it. I finished it in 19 lines but i think I did a few steps wrong. 1. B=W 2. L>B 3. ~Bv~W /~(WvL)

Algebra ->  Proofs -> SOLUTION: If you could help me with the problem I would really appreciate it. I finished it in 19 lines but i think I did a few steps wrong. 1. B=W 2. L>B 3. ~Bv~W /~(WvL)      Log On


   

Question 199553: If you could help me with the problem I would really appreciate it. I finished it in 19 lines but i think I did a few steps wrong.
1. B=W
2. L>B
3. ~Bv~W /~(WvL)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm going to use "<->" for "if and only if" and "*" for "and" 

1.   B <-> W
2.   L -> B
3.   ~B v ~W           :.  ~(W v L)
-----------------------------------
4.   (B -> W) * (W -> B)             1      Material Equivalence
5.   (W -> B) * (B -> W)             4      Commutation
6.   B -> W                          4      Simplification
7.   W -> B                          5      Simplification
8.   B -> ~W                         3      Material Implication
9.   W -> ~W                       7,8      Hypothetical Syllogism
10.   ~W v ~W                        9      Material Implication
11.  ~W                             10      Tautology
12.  ~B                           6,11      Modus Tollens
13.  ~L                           2,12      Modus Tollens
14.  ~W * ~L                     11,13      Conjunction 
15.  ~(W v L)                       14      De Morgan's Law