SOLUTION: 1. (R v S) > (H & ~G) 2. (K v R)

SOLUTION: 1. (R v S) > (H & ~G) 2. (K v R) > (G v ~H) / ~R

Question 1008772: 1. (R v S) > (H & ~G)
2. (K v R) > (G v ~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

-----------------------------------------------------------------------------

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
RELATED QUESTIONS
i need help solving this indirect proof 1. (R v S) > (H & ~G) 2. (K v R) > (G v ~H) (answered by Edwin McCravy)

solve plz? with rules of inference and replacement... 1. (~D + A) v (~D + R) 2. D v... (answered by math_tutor2020)

Premises: 1.) S->~(N v R) 2.) R v N v O 3.) ~O Conclusion:... (answered by Edwin McCravy)

(RvS) > (H & ~G) (k v r) > (G v ~H) /~R question2 n>r o<>r (o>r)>L /(n>o)&L (answered by solver91311)

I can only use the 8 implicational rules 1. (A v ~B) >(F v (R . G)) 2. A 3. F > L 4. (answered by jim_thompson5910)

Need help solving this proof: 1. ~O � K 2. ~O >(~R v A) 3. (~R > ~W) � (A > G) 4.... (answered by jim_thompson5910)

V= 1/3pie (r +r )^2 + (r + r ) h (answered by Alan3354)

1. M -> (R ^ E) 2. (E v H) -> G /M ->... (answered by Edwin McCravy)

Solve for v.... (answered by jim_thompson5910)