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Reasoning and Proof

Learning tasks
                                
Lesson Summary
Text book
Exercises Correction
A) Logical Connectives and Propositions
    I) Proposition
      1) Determining Truth ValuesEx 1 Ex 2 Ex 3 Ex 4 Ex 5 Ex 6 Ex 7
      2) Deducing Truth ValuesEx 8 Ex 9 Ex 10 Ex 11
    II) Negation
      3) Finding the Negation of a PropositionEx 12 Ex 13 Ex 14 Ex 15 Ex 16
      4) Deducing Truth ValuesEx 17 Ex 18 Ex 19
    III) Compound Propositions
      5) Evaluating Compound PropositionsEx 20 Ex 21 Ex 22 Ex 23
      6) Negating Conjunctions and DisjunctionsEx 24 Ex 25 Ex 26 Ex 27
    IV) Implication and Equivalence
      7) Identifying Related ImplicationsEx 28 Ex 29 Ex 30 Ex 31 Ex 32
      8) Writing the Converse and ContrapositiveEx 33 Ex 34 Ex 35
      9) Translating Statements into ImplicationsEx 36 Ex 37 Ex 38
    V) Quantifiers
      10) Evaluating Quantified StatementsEx 39 Ex 40 Ex 41
      11) Negating Quantified StatementsEx 42 Ex 43 Ex 44
      12) Translating Statements into Quantified FormEx 45 Ex 46 Ex 47
B) Written Proof
    I) Structure for Written Proofs
      13) Analyzing Proof StructuresEx 48 Ex 49 Ex 50
    II) Introducing a Variable
      14) Structuring a ProofEx 51 Ex 52 Ex 53
C) Methods of Proof
    I) Direct Proof (Proof by Deduction)
      15) Writing Direct Proofs in ArithmeticEx 54 Ex 55 Ex 56 Ex 57
      16) Constructing Direct Proofs in Various ContextsEx 58 Ex 59 Ex 60 Ex 61
      17) Constructing Direct Proofs: Proving a Statement is TrueEx 62 Ex 63 Ex 64
    II) Proof by Contrapositive
      18) Constructing Proofs by ContrapositiveEx 65 Ex 66 Ex 67
    III) Proof by Exhaustion (Cases)
      19) Constructing Proofs by ExhaustionEx 68 Ex 69 Ex 70 Ex 71
    IV) Disproof by Counterexample
      20) Disproving Statements by CounterexampleEx 72 Ex 73 Ex 74
    V) Proof by Equivalence
      21) Constructing Proofs of EquivalenceEx 75 Ex 76 Ex 77 Ex 78
      22) Constructing and Analyzing Proofs by Equivalence For IdentitiesEx 79 Ex 80 Ex 81 Ex 82
    VI) Proof by Contradiction
      23) Analyzing the Structure of Proof by ContradictionEx 83 Ex 84
      24) Constructing Proofs by ContradictionEx 85 Ex 86 Ex 87
    VII) Proof by Mathematical Induction
      25) Proving Inequalities by InductionEx 88 Ex 89 Ex 90
      26) Proving Sums of Powers by InductionEx 91 Ex 92 Ex 93
      27) Proving Sequence Properties by InductionEx 94 Ex 95 Ex 96
      28) Proving Divisibility Properties by InductionEx 97 Ex 98 Ex 99