SOLUTION: 1.) (K>K) > R 2.) (RvM) > N /N I need to use either AIP or ACP (or both) and the eighteen rules of inference to derive the conclusion. If someone can please help.

Algebra ->  Proofs -> SOLUTION: 1.) (K>K) > R 2.) (RvM) > N /N I need to use either AIP or ACP (or both) and the eighteen rules of inference to derive the conclusion. If someone can please help.      Log On


   

Question 536807: 1.) (K>K) > R
2.) (RvM) > N /N
I need to use either AIP or ACP (or both) and the eighteen rules of inference to derive the conclusion. If someone can please help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since we have the conclusion N, let's assume for the sake of argument that the opposite is true. In other words, let's assume that the conclusion is ~N. Our job is to show that a contradiction will arise, and if it does, then the opposite of ~N must be true (ie N is really the correct conclusion). 

1.) (K > K) > R
2.) (R v M) > N                     / N
----------------
	3.)  ~N                     AIP
	4.)  ~(R v M)        2,3    Modus Tollens
	5.)  ~R & ~M         4      De Morgan's Law
	6.)  ~R              5      Simplification
	7.)  ~(K > K)        1,6    Modus Tollens
	8.)  ~(~K v K)       7      Material Implication
	9.)  ~~K & ~K        8      De Morgan's Law
	10.) K & ~K          9      Double Negation
11.) N                       3-10   IP