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.

Analogy — Think of statement-conclusion logic like a strict courtroom standard, not everyday conversation. In everyday speech, "All doctors are rich" and "some doctors are poor" would feel contradictory — but in formal logic, "All A are B" says nothing at all about anyone who ISN'T an A, so it doesn't actually rule out other unrelated facts about non-doctors. The single biggest trap in this topic is importing real-world assumptions ("that seems unlikely, so it probably doesn't follow") into a system that only cares about strict logical validity — a conclusion either follows from EXACTLY what's stated, or it doesn't, regardless of whether it sounds true in real life.

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

1.Read the relationship statements carefully.

2."All A are B" = A inside B.

3."No A is B" = A and B separate.

4."Some A are B" = A and B partially overlap.

5.Draw accordingly. Match with given options.

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

1.Identify type of each statement (All/No/Some).

2.Apply rules to derive possible conclusions.

3.Check each conclusion against rules.

4."Either I or II" conclusion: only when I and II are complementary and one must be true.

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.

Revision Notes

VENN DIAGRAM RELATIONSHIPS:
All A⊆B: A circle inside B circle
No A-B: Circles separate
Some A,B: Circles partially overlap

3-CIRCLE APPROACH:
Draw relationship between each pair first
Then combine into one diagram

STATEMENT-CONCLUSION:
All A→B: "Some B are A" follows | "All B are A" does NOT
No A-B: symmetric | "Some A are not B" follows
Some A-B: "Some B are A" follows | "All A are B" does NOT

COMBINATION:
All+All can give All conclusion
Some+Any = usually only Some conclusion
Part+Part = generally no conclusion

Try It (2 Minutes)

Statement: "All pens are pencils." Conclusion: "Some pencils are pens." Before checking the rule above, draw two circles — a small one for Pens fully inside a larger one for Pencils (since ALL pens are pencils). Now look at your own diagram: does the Pencils circle necessarily contain at least some Pens? Yes — because the entire Pens circle sits inside it. That's exactly why "All A are B" always yields "Some B are A" as a valid conclusion, and you just derived it from your own drawing instead of memorizing it as a rule.