Section 3.6 Euler Diagrams and Syllogistic Arguments

• Syllogistic arguments are arguments of the form

• All national parks are beautiful.
  Zion is a national park.
  Therefore Zion is beautiful.
  

• In general we look at statements and conclusions in the form
  • All ______ are _____
  • Some _____ are ______
  • No ______ are ______
  • Some ____ are not _____
• We will use a technique attributed to Leonhard Euler.
  • 
  • Leonhard Euler (1707 to 1783) my 9^{th great academic ancestor.}
  • An astounding mathematician.
  • Major contribution to many fields. in many fields.
• We tend to solve these by drawing an Euler Diagram.
  • These predated Venn diagrams.
  • They only show relevant relationships.
  • 
• For each set in the argument add it to the Euler diagram.
• For individual items, try to draw a dot that meets the criteria, but does not match
• Do examples page 150