Chapter 4: Venn Diagrams for Immediate Inferences (Symbolic Logic)

venn diagram

a diagram that uses interlocking circles to represent classes

emptiness

nothing exists in the shaded area

What does shading indicate in a Venn Diagram?

SOMETHING exists in that area

What does an X in an area indicate in a Venn Diagram?

no information about that area

What does having no marks indicate in a Venn Diagram?

A Statement Venn Diagram (Modern View)

E Statement Venn Diagram (Modern View)

I Statement Venn Diagram (Modern View)

O Statement Venn Diagram (Modern View)

diagram its contradiction

What do you do when a categorical statement starts with “it is false that?”

• A and O Statements contradict each other

• E and I Statements contradict each other

What pairs of statements contradict each other?

1. Diagram the premise.

2. Ask: Is the information in the conclusion already in the premise’s diagram?

   If yes, the argument is valid

   If no, the argument is invalid

Steps to Test an Immediate Inference Using a Venn Diagram

reduce the number of classes WITHOUT changing the content of the argument by using one (or more) of the operations from chapter 3

Ex:

• Conversion

• Contraposition

• Contradiction

• Obversion

What do you do when more than 2 classes are mentioned (in an immediate inference) because there’s a reference to one or more class components?