Section 1.2: Inductive and Deductive Reasoning

1.2 Outline

  1. Magic squares
  2. A pattern of nines
  3. Order of operations (see below)
  4. Inductive reasoning (see below)
    1. conjecture
    2. exponentiation
      1. b2; b squared
      2. b3; b cubed
  5. Deductive reasoning (see below)
    1. undefined terms
    2. axioms or premises
    3. conclusion
    4. syllogism
    5. invalid reasoning
    6. Euler circles (see below)

1.2 Essential Ideas

Order of Operations

The order of operations in this section permeates almost all types of mathematical calculations. You should remember these steps:

First, perform any operations enclosed in parentheses.
Next, perform multiplication and divisions as they occur by working from left to right.
Finally, perform additions and subtractions as they occur by working from left to right.

Inductive Reasoning
The type of reasoning in which you first observe a pattern, and then predict outcomes for future occurrences.

Deductive Reasoning The type of reasoning involves reaching a conclusion by using a formal structure based on a set of undefined terms and a set of accepted unproved axioms or premises.

Euler Circles Test the validity of a syllogism by using Euler circles.