1. Section 3.6 Reasoning and Patterns

2. Deductive Reasoning Deductive reasoning starts with a general rule, which we know to be true. Then from that rule, we make a conclusion about something specific. Example: All turtles have shells The animal I have captured is a turtle I conclude that the animal in my bag has a shell

3. Inductive Reasoning Inductive reasoning is making a conclusion based on a set of empirical data. If I observe that something is true many times, I can conclude that it will be true in all instances. Example: All sheep that I've seen are white All sheep must be white

4. Induction vs. Deduction Two basic kinds of argument: inductive and deductive. Induction is usually described as moving from the specific to the general. Deduction begins with the general and ends with the specific. Arguments based on experience or observation are best expressed inductively, while arguments based on laws, rules, or other widely accepted principles are best expressed deductively.

5. Inductive Patterns Inductive reasoning is the process of looking for patterns Examples: 2, 4, 7, 11, 16, 22, 29 What is the pattern? Find the next two numbers.

6. Examples 96, 94, 90, 84, 76, 66, 54, ___, ____ 26, 27, 30, 35, 42, 51, 62, ___, ____ 14, 24, 33, 41, 48, 54, 59, ___, ____ 1, 2, 4, 8, 10, 20, 22, 44, ____, ____