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UGC NET PAPER 1 · UNIT 06 · MODULE 3: WESTERN LOGIC: INDUCTION, ANALOGY AND VENN DIAGRAMS · TOPIC 8

Venn Diagrams and Testing Validity

Draw the four propositions, test a syllogism by diagramming its premises, and read everyday class relations from Euler diagrams.

  • 4 sub-topics
  • 2 min read
  • Topic 8 of 19

What this topic covers

4 sub-topics, in the order to study them. Tap one to jump to it.

  1. 8.1BasicsVenn diagrams (John Venn ) represent classes as overlapping circles.
    • Venn
    • Boolean
    • 4 regions
    • 8 regions
    • Shading
  2. 8.2Diagramming the four propositionsProposition Diagram A: All S is P Shade the part of S outside P E: No S is P Shade the overlap of S and P I: Some S is P Put an X in the overlap O: Some S is not P Put an X…
    • outside
    • overlap
  3. 8.3Testing a syllogismCovers universal, Do not diagram the conclusion, valid.
    • universal
    • Do not diagram the conclusion
    • valid
    • invalid
    • Worked example
  4. 8.4Euler diagrams and everyday class relationsEuler diagrams show only the actual relationship between classes: one circle inside another (all S is P), separate circles (no S is P), overlapping circles (some S is P)…
    • actual

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8.1Basics#

In brief

Venn diagrams (John Venn ) represent classes as overlapping circles.

  • Venn
  • Boolean
  • 4 regions
  • 8 regions
  • Shading
  • empty
  • at least one member

Venn diagrams (John Venn) represent classes as overlapping circles. They follow the Boolean interpretation. A two-circle diagram has 4 regions (including outside); a three-circle diagram has 8 regions.

  • Shading an area means the area is empty.

  • An X means the area has at least one member.

  • An X on a boundary line means the member is in one of the two regions, but it is unknown which.

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8.2Diagramming the four propositions#

In brief

Proposition Diagram A: All S is P Shade the part of S outside P E: No S is P Shade the overlap of S and P I: Some S is P Put an X in the overlap O: Some S is not P Put an X…

  • outside
  • overlap
Proposition Diagram
A: All S is P Shade the part of S outside P
E: No S is P Shade the overlap of S and P
I: Some S is P Put an X in the overlap
O: Some S is not P Put an X in S outside P

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8.3Testing a syllogism#

In brief

Covers universal, Do not diagram the conclusion, valid.

  • universal
  • Do not diagram the conclusion
  • valid
  • invalid
  • Worked example
  • Existential fallacy

  1. Draw three overlapping circles labelled S, P and M.

  2. Diagram the universal premise first (shading), then the particular premise (X).

  3. Do not diagram the conclusion.

  4. Check whether the conclusion is already shown. If yes, the syllogism is valid; if not, it is invalid.

  5. When an X can fall in two regions, place it on the line; a conclusion needing the X in a definite region is then not established.

Worked example. All A are B; All B are C; therefore All A are C. Shade A outside B; shade B outside C. The part of A outside C is then fully shaded, so the conclusion is already shown. Valid (Barbara).

Existential fallacy: because Venn diagrams use the Boolean view, a syllogism needing existential import (for example AAI-1, universal premises with a particular conclusion) shows as invalid on the diagram.

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8.4Euler diagrams and everyday class relations#

In brief

Euler diagrams show only the actual relationship between classes: one circle inside another (all S is P), separate circles (no S is P), overlapping circles (some S is P)…

  • actual

Euler diagrams show only the actual relationship between classes: one circle inside another (all S is P), separate circles (no S is P), overlapping circles (some S is P), identical circles (same members).

Standard class-relation patterns (frequent in exams):

  • Dog, Cat, Animal: two separate circles inside a larger circle.

  • Mother, Sister, Woman: two overlapping circles inside the Woman circle (a woman may be both).

  • Doctors, Women, Teachers: the circles overlap each other as the data allow; test each stated relation.

  • Man, Woman, Human: two separate circles inside the Human circle.

  • Tiger, Lion, Carnivore: two separate circles inside the Carnivore circle.

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Test yourself on Venn Diagrams and Testing Validity

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↑ Module 3: Western Logic: Induction, Analogy and Venn Diagrams · All 19 topics in Logical Reasoning · Unit overview and sample MCQs

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