CS103 HO#9 More proofs, SAT Solving4/6/111CS103Mathematical Foundations of Computing4/6/11MondayKevin10 - 12Gates 200Bob3:45 - 5:00Gates 178TuesdayRyan1:15 - 3:15???Hrysoula7 - 9Gates B12WednesdayConal12:15 - 2:15Gates 200Bob3:45 - 5:30Gates 178ThursdayEvan2:15 - 4:15Gates 400Mingyu7 - 9200-201SundayNeel1 - 3Gates B12Karl5 - 7Gates B12Office HoursProof by ContradictionIndirect ProofSuppose ¬Q......¬SContradiction: S and ¬SQ S......Trying to prove QS is a premise or aderived statementSuppose nis prime and n> 2. Prove that nis odd.PROOF by contradiction:Suppose that nis even.Then there is an integer ksuch that n= 2k, and since n> 2, k> 1.But that means that nis divisible by 2 and k, and thusnis not prime, contradicting the hypothesis.Thus nmust be odd. ■nis prime n> 2Suppose nis evenThen n= 2kfor some integer k3, def. of even k> 12, 4 algebranis divisible by 2 and k4, def. of dividesnis not prime5, 6 def. of primeContradiction1, 7nis odd3 - 8123456789So ¬Q follows from P1, …, PnProof by ContradictionIndirect ProofSuppose that from premises P1, …, Pnwe wish to show ¬Q.One possibility is to temporarily assume Q, and see ifwe can show that P1, …, Pn, Q is impossible, i.e., thatthese claims can’t be true simultaneously.Then in any circumstances where P1, …, Pnare true, Q is false¬Q is true
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