Question

why are three circles required in proving argument by Venn diagram?​

Answer 1

Answer:

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Answer 2

Ans:

To test the validity of a categorical syllogism, one can use the method of Venn diagrams. Since a categorical syllogism has three terms, we need a Venn diagram using three intersecting circles, one representing each of the three terms in a categorical syllogism. A three term diagram has eight regions (the number of regions being 2n where n is the number of terms).

The following chart gives the extension of the predicates in the various regions of the diagram.

Region S (Minor Term) P (Major Term) M (Middle Term)

1 yes no no

2 yes yes no

3 no yes no

4 yes no yes

5 yes yes yes

6 no yes yes

7 no no yes

8 no no no

In order to use a Venn diagram to test a syllogism, the diagram must be filled in to reflect the contents of the premises. Remember, shading an area means that that area is empty, the term represented has no extension in that area. What one is looking for in a Venn diagram test for validity is an accurate diagram of the conclusion of the argument that logically follows from a diagram of the premises. Since each of the premises of a categorical syllogism is a categorical proposition, diagram the premise sentences independently and then see whether the conclusion has already been diagramed. If so, the argument is valid. If not, then it is not.

Remember, one definition of validity is that the propositional (informational) content of the conclusion is already expressed in the premises. Venn diagram validity tests provide a graphic tool for using this approach to testing for validity. A categorical syllogism is valid if, but only if, a diagram of its premises produces a diagram that expresses the propositional content of its conclusion.

Begin the process by preparing a three term Venn diagram. As a convention, organize the diagram as above, 2 circles at the top of the diagram, one centered at the bottom. The upper left hand circle should represent the minor term (designated S as this term is the subject of the conclusion). The upper right hand circle should represent the major term (designated P as this term is the predicate of the conclusion). The lower circle should represent the middle term (designated M). Your diagram should look like this: