Wetzel

Math 155

1.1 – Inductive and Deductive Reasoning (Patterns)

Inductive Reasoning –

            Def.:  The process of arriving at a general conclusion based on observations of specific examples.

            Ex.:

                        Given the pattern:  3, 6, 18, 36, 108, 216, _____, ______

                        Find the missing numbers.

                        Specific Statements:      3 to 6               add 3

                                                                                    multiply by 2

                                                            6 to 18             add 12

                                                                                    multiply by 3

                                                            18 to 36           add 18

                                                                                    multiply by 2

                                                            36 to 108         add 72

                                                                                    multiply by 3

                                                            108 to 216       add 108

                                                                                    multiply by 2

                        General Statement:        Alternating back and forth, multiplying by 2, then multiplying by 3.

                        Conclusion:       The next two numbers will be:  648, 1296

Deductive Reasoning –

            Def.:  The process of proving a specific conclusion from one or more general statements.

            Ex.: 

                        General Statement:  Anybody caught cheating will be given a zero.

                        Specific Statement:  Sally was caught cheating.

                        Conclusion:  Sally will get a zero.

HW:  p.9 # 5-25odd, 31, 33