SOLUTION: Help! I need this badly. Use rules of inference and replacement. Thaaaanks! P > A X > B /(P v X) > (A v B)

Algebra ->  Proofs -> SOLUTION: Help! I need this badly. Use rules of inference and replacement. Thaaaanks! P > A X > B /(P v X) > (A v B)      Log On


   

Question 1089734: Help! I need this badly. Use rules of inference and replacement. Thaaaanks!
P > A
X > B
/(P v X) > (A v B)
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
1.   P—>A                    Premise
2.   X—>B                    Premise
3.   (P v X) —> (A v B)      This follows directly by Constructive Dilemma (CD)

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I think this proves it the long way…
—
1.   P—>A                    Premise
2.   X—>B                    Premise
3.   P v X                   Premise
::4.   P                       Assumption, start Conditional Proof (CP)
::5.   A                       4,1 Modus Ponens (MP)
::6.   A v B                   5 Addition (ADD)
::7.   X                       Assumption
::8.    B                      7,2 MP
::9.   A v B                   8 ADD          
10.  A v B                   1,2,3 Proof By Cases (PBC)  { Discharges CP assumptions }       
11.  (P v X) —> (A v B)      1,2  CP