SOLUTION: INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems. Use indirect proof: 1. (R &#8744; S) &#8835; (H � &#8764;G) 2. (K &#8744; R) &#8835

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Question 1010728: INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems.
Use indirect proof:
1. (R ∨ S) ⊃ (H � ∼G)
2. (K ∨ R) ⊃ (G ∨ ∼H)
/ ∼R
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Proof by contradiction

Number Statement Lines Used Reason
1 (R v S) -> (H & ~G)
2 (K v R) -> (G v ~H)
.: ~R
3 ~~R AIP
4 R 3 DN
5 R v S 4 Add
6 R v K 4 Add
7 K v R 6 Comm
8 H & ~G 1,5 MP
9 ~G & H 8 Comm
10 H 8 Simp
11 ~G 9 Simp
12 G v ~H 2,7 MP
13 ~H 12,11 DS
14 H & ~H 10,13 Conj
15 ~(~~R) 3-14 IP
16 ~R 15 DN

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Acronyms/Abbreviations Used

Add = Addition
AIP = Assumption for Indirect Proof
Comm = Commutation
Conj = Conjunction
DM = De Morgan's Law
DN = Double Negation
DS = Disjunctive Syllogism
IP = Indirect Proof (aka proof by contradiction)
MP = Modus Ponens
Simp = Simplification

SOLUTION: INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems. Use indirect proof: 1. (R &#8744; S) &#8835; (H � &#8764;G) 2. (K &#8744; R) &#8835

SOLUTION: INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems. Use indirect proof: 1. (R ∨ S) ⊃ (H � ∼G) 2. (K ∨ R) &#8835