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 |
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| 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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