Prove these arguements valid with the 17 rules of inference:*1) 1. (zx) . (x~z)2. zvx3. ~x /...

Question

Prove these arguements valid with the 17 rules of inference:*1) 1. (z>x) . (x>~z)2. zvx3. ~x / A.B*2) 1. Bv(S.N)2.B>~S3. S>~N/ BvW*3) 1. (Q.F) v R2. (QvR) >~P3. ~A / ~(AvP)*4) 1. A>~A/ ~A*5) 1. A>B2. C>B/ (AvC)>B*6) 1. S>R/ S>(RvT)*7) 1. ~A>(B>~C)2. ~D>(~C>A)3. Dv~A4. ~D/ ~B*8) 1. (S>B)>(SvK)2. (Kv~D)>(H>S)3. ~S.W/ ~H*9) 1. (Z.Y)>X2. ~O>Z3. ~Y>O4. ~O.T/ X*10) 1. F>G2. ~HvI3. (GvI)>J4. ~J/ ~(FvH)-The statements after the / is the conclusion and we must solve the proof
 using these rules to get to the conclusion and prove the overall 
argument valid.-Must also provide the justification number for each line in the proof.- The 17 rules of inference are:1) Modus Ponens2) Modus Tollens3)Disjunctive Syllogism4) Hypothetical Syllogism5) Constructive Dilemma6) Simplification7) Conjunction8) Addition9) DeMorgan's Rule10) Commutativity11) Associativity12) Distribution13)Transposition14)Material Implication15) Material Equivalence16) Exportation17) Tautology

Robert · Accepted Answer

Please note:
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This question is complete. Since the given expression is a contradiction, it implying any 
statement is a tautology 
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Prove these arguements valid with the 17 rules of inference: 1) 1. (z>x) . (x>~z) 2. zvx 3. ~x / A.B 2) 1. Bv(S.N) 2.B>~S 3. S>~N/ BvW 3) 1. (Q.F) v R 2. (QvR) >~P 3. ~A / ~(AvP) 4) 1. A>~A/ ~A...

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Prove these arguements valid with the 17 rules of inference: *1) 1. (z>x) . (x>~z) 2. zvx 3. ~x / A.B *2) 1. Bv(S.N) 2.B>~S 3. S>~N/ BvW *3) 1. (Q.F) v R 2. (QvR) >~P 3. ~A / ~(AvP) *4) 1. A>~A/ ~A...

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Prove these arguements valid with the 17 rules of inference: 1) 1. (z>x) . (x>~z) 2. zvx 3. ~x / A.B 2) 1. Bv(S.N) 2.B>~S 3. S>~N/ BvW 3) 1. (Q.F) v R 2. (QvR) >~P 3. ~A / ~(AvP) 4) 1. A>~A/ ~A...