prove usding indirect proof 1 PvQ p 2 RSN p 3 MvSR p 4 MvQ p

prove usding indirect proof:

1. -(PvQ) p

2. R>(S>N) p

3. Mv(S*R) p

4. -MvQ p / NvO

- = tilda * = and/or p = proof / assumed

1)~(PvQ)

~~(PvQ)=~(~P)^(~Q) = (P)^(~Q)

2)R>(S>N)

~[R>(~SvN)]=~[~Rv(~SvN)] = (R^~S)>~N

3)Mv(S^R)

~[Mv(S^R)] = M^(~[S^R]) = M^(S^~R) = (MvS)^(MvR)

4)~MvQ

~[~MvQ] = M>Q