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37 - Chapter-3 Renee at General Review Guide Chapter 3...

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Unformatted text preview: Chapter -3 Renee at General Review Guide: Chapter 3 Definitions o 1|iiihyiathephraee "if1andonl1rif‘ usedinadefinition? (p. 13?} I Howarethefiillowingtermsdelinsd? - even integer (p. 12’?) - Odd integer I'P- 13?) — prime number (1:. L93) — compositennmber (p. 1.93} — rational number (p. 141) — diviaihility,r of oneintegsr by another (1!. HS) ~— the floorofarealnumhsr (p. 165) — theeeiiing ofarealmamherfp.155} - greatest common divisor of two integers (p. 19.2} Proving an Existential Statementffliaproving a Universal Statement I How do you determine the truth of an existential statement? (p. 133} I What does it mean to “disprove“ a statement? (p. 139) I What is diaprocd by mummplo? (p. 13.9) I How do you establish the falsity of a universal statement? (p. 1129) Proving a Universal Statementfflisproving an Existential Statement I Ifauniversalatatementisdefinedoveraamall.finitedomain.tho}rouuaethemethodof exhaustion to prove that it is true? (p. 13H) I What is the method of geoeraiieiog from the generic particular? (p. 13:1] - Hyouusethemethodofdirectprooftoprovsastatementoftheform “Vic, ifPIE-e] thenQ{a)", what doyonsnpposeandwhat doyou have toehow?(p.131) I What are the guidelines iior writing proofs ofuniveraal statements? (p. 134‘) I What are some common mistakes people make when writing mathematical pct-oats? (p. 135) I How do you disptnve an existential statement? (p. 138} I What is the method of proof by division into cases? (p. 133) I Hymuaethemethadofproofhyeontradictiontoproveastatemsnt,whatdoyousuppcee' and what dovoahavetoahow?(p.1?1) I Hymnsethemethodofproofhvoontrapoaiflontoproveastatementoftheform Wa,i£P{e} then 0(a)“, what do you suppose and what do you have to show? (p. HE) a Are you ahleto usethevarious methods ofproofand disoroofto establish the truth orfalsitv of statements about odd and even integers (p. 133}, prime when (p. 133}, rational numbers (pp. Lid, 145, 1'45}? diviaihrilityr of integers (pp. 151-1533), and the floor and ceiling of a real 1111th (pp. 155-168)? ' der theorem? Can you appll.r it to specific situations? fill. 15?} I‘Whatisthequotient- theirratiooality ofthe square root ofi? Can you provathis I Wimt is the theorem about theorem? (p. 131) ...
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