Logical Reasoning — Venn Diagrams and Statement-Conclusion
Why This Chapter Matters
Venn diagrams and statement-conclusion questions appear in every SSC exam — 3-5 marks. Understanding inclusion/exclusion relationships and drawing correct diagrams is the key skill.
Part 1 — Venn Diagrams
Types of Relationships
All A are B: A's circle is INSIDE B's circle.
No A is B: Circles are completely separate (no overlap).
Some A are B: Circles partially overlap.
Some A are not B: Part of A is outside B.
3-Circle Venn Diagram Problems
Given: All doctors are engineers. Some engineers are teachers.
Draw: Teachers, Doctors, Engineers.
Doctors ⊆ Engineers. Engineers and Teachers partially overlap.
Correct diagram: Doctor circle inside Engineers. Teacher circle partially overlapping Engineers (but NOT necessarily overlapping Doctors — we're not told).
Best Represents Relationships
3 items given. Choose which Venn diagram correctly shows their relationship.
Example: Mammals, Cats, Dogs → All cats are mammals AND all dogs are mammals, but cats and dogs are separate → Two small circles (cats, dogs) both inside a large circle (mammals), not overlapping each other.
Example: Boys, Students, Athletes → Some boys are students, some are athletes, some students are athletes → Three overlapping circles (could all overlap partially).
Approach
Part 2 — Statement and Conclusion
Given a statement, find which conclusions logically follow.
Rules
Universal affirmative (All A are B):
Conclusion "Some A are B" → FOLLOWS (a subset statement).
Conclusion "All B are A" → Does NOT follow (converse is not given).
Conclusion "Some B are A" → FOLLOWS (if all A are B, some B must be A).
Universal negative (No A is B):
"No B is A" → FOLLOWS (negative is symmetric).
"Some A are not B" → FOLLOWS.
"Some A are B" → Does NOT follow.
Particular affirmative (Some A are B):
"All A are B" → Does NOT follow (stronger than given).
"Some B are A" → FOLLOWS.
Combined statements:
Universal + Universal can give universal or particular conclusion.
Particular + Particular → generally no valid conclusion.
Approach
Solved Examples
Q1 (Venn): Which figure best represents: Vegetables, Potato, Food?
All vegetables are food. All potatoes are vegetables (and hence food).
Potato ⊂ Vegetables ⊂ Food → Three concentric circles: Potato inside Vegetables inside Food.
Q2 (Statement-Conclusion):
Statement: All chairs are tables. No table is a cupboard.
Conclusion I: No chair is a cupboard.
Conclusion II: Some tables are chairs.
I: Chairs → Tables → Not cupboards. Chain valid. I FOLLOWS.
II: All chairs are tables → Some tables are chairs. II FOLLOWS. Both I and II follow.
PYQs (SSC)
SSC CGL 2023 (Venn): Which diagram shows relationship between: Flowers, Rose, Marigold?
Rose and Marigold are both types of flowers, but completely different from each other.
Diagram: Two small separate circles (Rose, Marigold) both inside a large circle (Flowers).
SSC CHSL 2022 (Statement):
Statements: Some cats are dogs. All dogs are animals.
Conclusion I: Some cats are animals. Conclusion II: All animals are dogs.
I: Some cats → dogs → animals. FOLLOWS. II: Converse of "all dogs are animals". Does NOT follow. Answer: Only I follows.