§ 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
  
• 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.
    
    Premise: You are in Oregon.
    Conclusion: ?
  • If you are in the United States, then you are in Oregon.
    
    Premise: You are in the US.
    Conclusion: ?
  • If you are NOT in Oregon, then you are NOT in the United States.
    
    Premise: You are NOT in Oregon.
    Conclusion: ?
  • If you are NOT in the United States, then you are NOT in Oregon.
    
    Premise: You are NOT in the US.
    Conclusion: ?