SOLUTION: write a direct proof using the eight rules of inference (C → Q) • (~L → ~R), (S → C) • (~N → ~L), ~Q • J, ~Q → (S v ~N), therefore, ~R i have t

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Question 1066422: write a direct proof using the eight rules of inference
(C → Q) • (~L → ~R), (S → C) • (~N → ~L), ~Q • J, ~Q → (S v ~N), therefore, ~R
i have to use the eight rules, but this particular problem is very hard for me. hoping you can help.
this is from the power of logic 5th edition.
these are the rules im being given.


Rule 1: Modus ponens (MP): p → q
p
∴ q
Rule 2: Modus tollens (MT): p → q
∼q
∴ ∼q
Rule 3: Hypothetical syllogism (HS): p → q
q → r
∴ p → r
Rule 4: Disjunctive syllogism (DS), in two forms:
p ∨ q p ∨ q
∼p ∼q
∴ q ∴ p
Rule 5: Constructive dilemma (CD): p ∨ q
p → r
q → s
∴ r ∨ s
Rule 6: Simplification (Simp), in two forms:
p • q p • q
∴ p ∴ q
Rule 7: Conjunction (Conj): p
q
∴ p • q
Rule 8: Addition (Add) in two forms:
p p
∴ p ∨ q ∴ q ∨ p
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!

 1.  (C → Q)•(~L → ~R)
 2.  (S → C)•(~N → ~L)
 3.  ~Q•J 
 4.  ~Q → (S v ~N)     /~R

 5. ~Q                              3, Simp
 6. S v ~N                        4,5, MP
 7. (S v ~N)•(S → C)•(~N → ~L)    6,2, Conj 
 8. C v ~L                          7, CD  
 9. (C v ~L)•(C → Q)•(~L → ~R)    8,1, Conj
10. Q v ~R                          9, CD
11. ~R                           10,5, DS

Edwin
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