Venn Diagrams & Syllogism
Syllabus Unit: General Intelligence & Reasoning
Why it matters
Chapter overview
Syllogism and Venn-diagram questions test formal logic: draw the circles for each premise and read the conclusion directly off the diagram rather than reasoning in words, which is where most errors creep in. This topic builds the diagram-first method for syllogisms, region-filling for numeric Venn problems, inequality-chain merging for analytical reasoning, and the most-constrained-clue-first approach for seating puzzles.
1Syllogisms & Statement-Conclusions
A syllogism is valid only if the conclusion follows from the given statements in EVERY possible diagram consistent with them — draw the least restrictive diagram to test validity.
Learning Objectives
- Draw the Venn diagram for each of the four standard categorical statements: All A are B, No A are B, Some A are B, Some A are not B.
- Apply the chain rule: 'All A are B' + 'All B are C' validly gives 'All A are C'.
- Test conclusion validity by attempting to draw a diagram that satisfies the premises but contradicts the conclusion.
- Distinguish 'possibility' conclusions from definite conclusions that the premises actually require.
Key Terms
Syllogisms reward diagram discipline over verbal reasoning — draw the circles for the premises, and read whether the conclusion is forced, possible, or impossible directly off the picture.
The four standard statement diagrams
- All A are B: circle A drawn entirely inside circle B.
- No A are B: circles A and B drawn completely separate, not touching.
- Some A are B: circles A and B drawn overlapping, with at least one shared region.
- Some A are not B: circle A drawn so part of it lies outside circle B.
Worked example
All pens are pencils; all pencils are erasers. Chaining gives: All pens are erasers (valid), and since pens are entirely inside erasers, Some erasers are pens is also necessarily true.