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Quantified Arguments and Venn Diagrams

Quantified Arguments and Venn Diagrams. All p are q Some p are not q Some p are q No p are q. p → q ~(p → q) or p ~q p q ~ (p q) or. Quantified Statements in Symbolic Form. Quantifiers and Sets. All P are Q implies P Q or P-Q= Some P are Q implies

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Quantified Arguments and Venn Diagrams

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  1. Quantified Arguments and Venn Diagrams

  2. All p are q Some p are not q Some p are q No p are q p → q ~(p → q) orp ~q p q ~ (p q) or Quantified Statements in Symbolic Form

  3. Quantifiers and Sets • All P are Q implies P Q or P-Q= • Some P are Q implies • Some P are not Q implies • No P and Q implies

  4. The shaded areas are empty. “All” and “No” quantifiers empty areas. Quantifiers and Venn Diagrams. All A are B No A are B

  5. “Some” and “Some are not” put something into the diagram. In the 3 circle diagrams the arrows indicate that the something could be in either area. Some A are B. More Quantifiers and Venn Diagrams Some A are not B

  6. Testing for Validity with Venn Diagrams Make a diagram for the situation, 2 or 3 circles. • Shade empty areas by the premises that have “all” or “no” in them. • Place a x in areas determined by the premises that use “some” or “some are not”.

  7. Premises No cat is slow. Some cats are hunters. Conclusion Some hunters are slow. 3 circles are needed. Set of cats Set of slow things Set of hunters Arguments and Venn Diagrams

  8. “No cat is slow” empties areas 1 and 2. “Some cats are hunters” puts something in area 3. Argument continued

  9. Is the Argument Valid? • From the diagram would you stake your life on the conclusion? • Some hunters are slow. • Remember you only know that areas 1 and 2 are empty and that area 3 is not empty. • To find a hunter that is slow you would go to area 5 but you know nothing about area 5. • The argument is invalid.

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