SOLUTION: (X^Y)v(T^R)/~~(RvY)

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Question 1038288: (X^Y)v(T^R)/~~(RvY)
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

You need commutation, distribution, 
constructive dilemma, and double negation

Commutation is

p^q <-> q^p

Distribution is

pv(q^r)<-> (pvq)^(pvr)

Constructive dilemma is

[(p->q)^(r->s)^(pvq)] -> (qvs)

Double negation

p <-> ~~p


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1.  (X^Y)v(T^R)      /~~(RvY)

2.  (X^Y)<->(Y^X)      Commutation

3.  (T^R)<->(R^T)      Commutation

4.  (Y^X)v(R^T)        1,2,3, Substitution

5.  (Y^X)->Y           Simplification

6.  (R^T)->R           Simplification

7.  YvR                5,6,1 Constructive dilemma

8.  RvY                7, Commutation

9.  ~~(RvY)            8, Double negation

Edwin