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...

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
*5) 1. A>B
2. C>B/ (AvC)>B
*6) 1. S>R/ S>(RvT)
*7) 1. ~A>(B>~C)
2. ~D>(~C>A)
3. Dv~A
4. ~D/ ~B
*8) 1. (S>B)>(SvK)
2. (Kv~D)>(H>S)
3. ~S.W/ ~H
*9) 1. (Z.Y)>X
2. ~O>Z
3. ~Y>O
4. ~O.T/ X
*10) 1. F>G
2. ~HvI
3. (GvI)>J
4. ~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 Ponens
2) Modus Tollens
3)Disjunctive Syllogism
4) Hypothetical Syllogism
5) Constructive Dilemma
6) Simplification
7) Conjunction
8) Addition
9) DeMorgan's Rule
10) Commutativity
11) Associativity
12) Distribution
13)Transposition
14)Material Implication
15) Material Equivalence
16) Exportation
17) Tautology