LR07 — Logical Venn Diagrams

🧠 AFCAT Reasoning · LR07 ✈️ AFCAT Level

📌 AFCAT Pattern (LR07): Venn Diagrams contribute 2–3 questions per paper. Two types: (1) Find the correct Venn diagram representing the relationship among given groups. (2) Find the count or region satisfying conditions. The critical skill is understanding inclusion relationships: “All A are B” vs “Some A are B” vs “No A is B.”

PART A — RELATIONSHIP TYPES AND DIAGRAMS

1. The 5 Fundamental Venn Relationships

Statement	Diagram Type	Example
All A are B	Circle A fully inside Circle B	All pilots are officers → Pilots circle inside Officers circle
No A is B	Two separate circles (no overlap)	IAF pilots and INS submarines → No overlap
Some A are B	Partially overlapping circles	Some athletes are soldiers → Partial overlap
Some A are B; Some A are not B	Partial overlap	Some officers are pilots; some are not
All A are B; All B are A	Identical circles / one circle	Synonyms (rare in AFCAT)

2. Choosing the Correct Venn Diagram

Method: Analyse Each Pair

Read the three given categories
Determine relationship between each PAIR (A-B, B-C, A-C)
Can members of group A ALSO be in group B?
Are the groups mutually exclusive or inclusive?
Draw the appropriate circle arrangement

AFCAT-Frequent Examples

IAF Officers, Pilots, Humans → Pilots ⊂ IAF Officers ⊂ Humans (nested 3 circles)
Soldiers, Athletes, Doctors → Partial overlaps (some can be in multiple)
Cricket, Football, Hockey → Separate circles (distinct sports)
India, Asia, World → India ⊂ Asia ⊂ World (nested)

3. Region-Based Count Problems

Two circles A and B. Total in A=40, Total in B=30, in Both=10. Find: (a) Only in A, (b) Only in B, (c) In at least one, (d) In neither (if total=100).

Worked Example

A=Pilots who have flown MiG-21 (40). B=Pilots who have flown Su-30MKI (30). Both=10.
Only A = 40−10 = 30. Only B = 30−10 = 20. At least one (A∪B) = 30+20+10 = 60. Neither (if total=100): 100−60 = 40.

📝 AFCAT PYQVenn Diagrams — AFCAT Pattern

Q1. Which Venn diagram best represents: IAF Officers, Air Marshals, Citizens of India? (AFCAT I 2025)

(a) All three separate circles
(b) Air Marshals inside IAF Officers; both inside Citizens of India
(c) IAF Officers inside Air Marshals; both inside Citizens
(d) All three overlapping partially

Answer: (b) Air Marshals ⊂ IAF Officers ⊂ Citizens of India
All Air Marshals are IAF Officers (Air Marshal is a rank in IAF — All Air Marshals are officers). All IAF Officers are Citizens of India (you must be a citizen to serve). Therefore: nested circles — smallest = Air Marshals, middle = IAF Officers, largest = Citizens of India.

Q2. In a group of 100 soldiers: 60 can operate aircraft, 50 can operate submarines. 20 can operate both. How many can operate neither? (AFCAT II 2024)

(a) 10
(b) 20
(c) 30
(d) 40

Answer: (a) 10
A∪B = A + B − A∩B = 60 + 50 − 20 = 90. Neither = Total − A∪B = 100 − 90 = 10. Formula: Total = Only A + Only B + Both + Neither → 40 + 30 + 20 + Neither = 100 → Neither = 10.

Q3. Which Venn diagram correctly represents: Rectangles, Squares, Quadrilaterals? (AFCAT I 2024)

(a) Three separate circles
(b) Squares inside Rectangles; Rectangles inside Quadrilaterals
(c) Rectangles inside Squares; both inside Quadrilaterals
(d) Partial overlaps among all three

Answer: (b) Squares ⊂ Rectangles ⊂ Quadrilaterals
All squares are rectangles (special case with equal sides). All rectangles are quadrilaterals (4-sided polygons). Therefore: Squares circle is INSIDE Rectangles circle, which is INSIDE Quadrilaterals circle. This is a 3-level nested Venn diagram.

⚡ Quick Reference — LR07

Diagram Types

All A are B → A inside B
No A is B → separate circles
Some A are B → partial overlap
Nested: A⊂B⊂C → 3 concentric circles

Count Formula

A∪B = A + B − A∩B
Only A = A − Both
Neither = Total − A∪B
Three sets: A+B+C−AB−BC−AC+ABC

AFCAT Favourite Sets

Rank hierarchies (Air Marshal ⊂ Officers)
Geographic (City ⊂ State ⊂ Country)
Species (Mammals ⊃ Dogs)
Geometric (Squares ⊂ Rectangles)

📝 AFCAT Mock Tests 🎯 Reasoning Quiz ✈️ Telegram