Chapter 2 – Logic, Proof, and Arguments

Chapter 2 – Logic,Proof, and ArgumentsChapter 2:- Identify the hypothesis and conclusion in a statement and be able to write the converse,inverse, contra-positive, and bi-conditional statements.- Compare and contrast undefined terms, postulates, definitions, and theorems.- Analyze the validity of a deductive argument (i.e. counterexamples)- Develop a logical conjecture using prior observations such as interior and exterior angle sums ina polygon.- Prove conjectures in paragraph format, flow diagram, or two-column format.- Use proof by contradiction (indirect proof) to prove conjectures

Standard 2.1 –- Identify the hypothesis and conclusion in a statement and be able to write the converse,inverse, contra-positive, and bi-conditional statements.RubricTask: Given a statement write an IF, THEN statement from the original statement. After youhave written the IF, THEN statement, identify the hypothesis and conclusion. From the IF, THENwrite all of the parts of our bi-conditional and conditional statements.0 1 2 3Correct IF,Did not write anWrote an IF,Wrote an IF,Wrote a correctTHENstatementIF, THENstatement.THEN statementthat did notpertain to theTHEN statementbut flipped theIF and THENIF, THENstatement fromthe originaloriginalparts.statement.statementIdentificationDid not IdentifyIdentified theIdentified theIdentified bothof theHypothesisandConclusioncorrectly boththe hypothesisAND theconclusioncorrecthypothesis butthe incorrectconclusion.correctconclusion butthe incorrecthypothesisthe hypothesisAND conclusioncorrectly.Bi-conditionalDid not write aWrote a bi-Wrote a CorrectstatementpartsBi-Conditionalconditional in anIF, THEN formBi-conditional.ConditionalDid not createCreated one ofCreated two ofCreated all threestatementpartsany of thefollowing:Inverse,the following:Inverse,Converse, orthe following:Inverse,Converse, orof the following:Inverse,Converse, ANDConverse, orContra-positiveContra-positiveContra-positiveContra-positive.

Standard 2.2 –- Compare and contrast postulates, definitions, and theorems.Task: Find the definitions for postulates, definitions and theorems then journal in your portfoliohow postulates, definitions and theorems differ. Make sure you address all of three of themand describe in your own words what they mean.Rubric0 1 2 3Analysis ofDid not compareOnly talkedTalked aboutTalked about allthevocabularyand contrast anyof the wordsabout one of thethree wordstwo of thewordsthree of thewordsDefinitions ofDid not defineDefined one ofDefined two ofDefined alltheany of the wordsthe three wordsthe three wordsthree.vocabulary

Standard 2.3- Develop a logical conjecture using prior observations such as interior and exterior angle sums ina polygon.Task: Given an interior and exterior angles, come up with one conjecture and prove it using anymethod that you know.Rubric0 1 2 3ConjectureDid not come upConjecture hadConjecture waswith anothing to dowell written andconjecturewith interior orhad to do withexterior angles.interior orexterior angles.Proof No Proof Proof wasincorrect, it didnot prove theconjectureProof wasmostly correctbut a few gapsin logicProof wasperfect

Standard 2.4- Prove conjectures in paragraph format, and flow format.Task: Write a paragraph showing how you know that the sun will rise every morning. Use thesame idea to write a flow diagram.Rubric0 1 2 3ParagraphDid not writeParagraph has aParagraph has aParagraphProofthe proof inparagraph formgood thesis butthe logic doesgood thesis witha goodproves that thesun will risenot fit and thereconclusion butevery morningis no conclusionmissing somewithout anylogic stepslogic gapsFlow ProofDid not use aFlow has a goodFlow has a goodFlow proves thatflow method tothesis but thethesis with athe sun will riseprove.logic does not fitgood conclusionevery morningand there is nobut missingwithout anyconclusionsome logic stepslogic gaps

Standard 2.5Use proof by contradiction (indirect proof) to prove conjecturesTask: Given a proof describe what is wrong with the logic, and fix it to make the proof correct.Rubric0 1 2 3IdentificationDid not find aFound 1 of the 3Found 2 of the 3Found all of theof theproblemproblems withthe proofproblemsproblemsproblemsCorrect fixDid not fix theFixed 1 of the 3Fixed 2 of the 3Fixed all of theproof, left it as isproblemsproblemsproblems