MTH211 Foundations of Elementary Math 1

the one percent

Fun with whole numbers.

Notes on Whole Numbers
Fall 2019

§ 2.2 Introduction to Deductive Reasoning

Main Topics

  • Deductive Reasoning:
    the process of forming conclusions from one or more given statements
  • Statements: Premise and Conclusions
  • Venn Diagrams
    proper subset
  • Conditional Statements: If p, then q. `p implies q`
  • Converse: If q, then p. `q implies p`
  • Inverse: If not p, then not q. `not p implies not q`
  • Contrapositve: If not q, then not p. `not q implies not p`
  • Examples:
    • If you are in Oregon, then you are in the United States.
      if Oregon, then US.
      Premise: You are in Oregon.
      Conclusion: ?
    • If you are in the United States, then you are in Oregon.
      if Oregon, then US.
      Premise: You are in the US.
      Conclusion: ?
    • If you are NOT in Oregon, then you are NOT in the United States.
      if Oregon, then US.
      Premise: You are NOT in Oregon.
      Conclusion: ?
    • If you are NOT in the United States, then you are NOT in Oregon.
      if Oregon, then US.
      Premise: You are NOT in the US.
      Conclusion: ?

Math Activity 2.2: Deductive Reasoning Game

  • Two Players
  • One picks a number; the other tries to guess.
  • Pica: A digit that is correct but not in the correct position.
  • Centro: A digit that is correct and in the correct position.

example?