2.1 Using Inductive Reasoning to Make Conjectures

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Using Inductive Reasoning to Make Conjectures 2-1

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2.1 Using Inductive Reasoning to Make Conjectures

Inductive Reasoning Inductive Reasoning- the process of reasoning that a rule or statement is true because specific cases are true. Inductive Reasoning 1) Look for a pattern. Make a conjecture. 3) Prove the conjecture true or find a counterexample.

Patterns Pattern- an arrangement or sequence in objects or events Examples: Find the next item in each pattern. January, March, May, … 7, 14, 21, 28, … , , … 0.4, 0.04, 0.004, …

Conjecture Conjecture: A statement you believe to be true based on inductive reasoning Examples: Complete each conjecture. The sum of two positive number is ___________. The number of lines formed by 4 points, no three of which are collinear, is ______________. The product of two odd numbers is ____________.

Example: The cloud of water leaving a whale’s blowhole when it exhales is called its blow. A biologist observed blue-whale blows of 25 ft, 29 ft, 27 ft, and 24 ft. Another biologist recorded humpback-whale blows of 8 ft, 7 ft, 8 ft, and 9 ft. Make a conjecture based on the data.

True or False Conjectures To show a conjecture is true, you must prove it. To show a conjecture is false, you must find only one example that is not true Counterexample: An example that proves a conjecture or example is false. Counterexamples can be a drawing, a statement, or a number

Examples: Show that each conjecture is false by finding a counterexample For every integer n, n3 is positive. Two complementary angles are not congruent. For any real number x, x2 > x. Supplementary angles are adjacent.