This final week of new work is focused on aspects of logic and logical methods of thinking and problem solving.

One important area is inductive and deductive reasoning. We use these types of reasoning to draw conclusions or make decisions or solve problems.

Chapter 1 section 1-1 in the e-text presents information about these two types of reasoning.

After carefully studying this section respond to the below tasks in the context of Math 105:

Provide an example in the context of Math 105 of a conclusion or decision you made based on inductive reasoning. Explain why inductive reasoning was involved.
Provide an example in the context of Math 105 of when you used deductive reasoning. Explain why this was a use of deductive reasoning.

E-book
This is an example of inductive reasoning. By observing certain events for four specific Fridays, you arrive at a general conclusion. Inductive reasoning is useful in everyday life, and it is also useful as a problem-solving tool in math, as shown in Example 1.

Example 1
Using Inductive Reasoning to Find a Pattern
A game show contestant is given the following string of numbers:

1, 2, 4, 5, 7, 8, 10, ____, ____, ____

She’ll win $1,500 if she can continue the pattern and fill in the three blanks. Use inductive reasoning to find a correct answer. How confident are you in your answer? 100%? Or less than that?

SOLUTION
To find patterns in strings of numbers, it’s often helpful to think about operations that can turn a number into the next one. In this case, we can use addition to find a regular pattern:

The pattern seems to be to add 1, then add 2, then add 1, then add 2, etc. So a reasonable conjecture for the next three numbers is 11, 13, and 14.

Now let’s talk about confidence. I like this answer a lot, but I’m not 100% confident. I made an educated guess based on just seven numbers. There’s no guarantee that this is the ONLY correct answer.