SOLUTION: Derive: A v ~B 1.(F v G) v (A v ~B) 2. F>A 3. B>~G

Question 1009334: Derive: A v ~B
1.(F v G) v (A v ~B)
2. F>A
3. B>~G
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Proof by contradiction

Number		Statement	Lines Used	Reason
1		(F v G) v (A v ~B)
2		F -> A
3		B -> ~G
.:		A v ~B
	5	~(A v ~B)		AIP
	6	~A & ~~B	5	DM
	7	~A & B	6	DN
	8	B & ~A	7	Comm
	9	~A	7	Simp
	10	B	8	Simp
	11	~F	2,9	MT
	12	~G	3,10	MP
	13	~F & ~G	11,12	Conj
	14	~(F v G)	13	DM
	15	A v ~B	1,14	DS
	16	~B	15,9	DS
	17	B & ~B	10,16	Conj
18		A v ~B	5-17	IP

Acroynyms/Abbreviations used

AIP = assumption for indirect proof
Comm = commutation
Conj = conjunction
IP = indirect proof
DM = de morgan's law
DN = double negation
DS = disjunctive syllogism
MP = modus ponens
MT = modus tollens
Simp = simplification
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