SOLUTION: 1. A > [B>(C*~D)] 2. (BvE)>(DvE) Therefore, 3. (A*B) > (C*E) Using conditional proof and 18 rules derive the conclusion to prove it is valid

Algebra ->  Proofs -> SOLUTION: 1. A > [B>(C*~D)] 2. (BvE)>(DvE) Therefore, 3. (A*B) > (C*E) Using conditional proof and 18 rules derive the conclusion to prove it is valid      Log On


   

Question 582129: 1. A > [B>(C*~D)]
2. (BvE)>(DvE)
Therefore,
3. (A*B) > (C*E)
Using conditional proof and 18 rules derive the conclusion to prove it is valid
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

1.   A > [B > (C * ~D)]
2.   (B v E) > (D v E)           /    (A*B) > (C*E) 
---------------------------------------------
3.   A * B       Conditional Proof(assume antecedent of conclusion is true)
4.   B * A                       3       Commutation
5.   A                           3       Simplification
6.   B                           4       Simplification
7.   B > (C * ~D)                1,5     Modus Ponens
8.   C * ~D                      7,6     Modus Ponens
9.   C                           8       Simplification
10.  ~D * C                      8       Commutation
11.  ~D                          10      Simplification
12.  B v E                       6       Addition
13.  D v E                       2,12    Modus Ponens
14.  E                           13,11   Disjunctive Syllogism  
15.  C * E                       9,14    Conjunction