Module 2: S4 Reasoning
Topic 2: Syllogisms & Venn Diagrams
1 The Foundation: 4 Pillars of Logic
Every syllogism in the UPSC exam is built from four standard categorical propositions. Memorize their minimum-overlap Venn diagrams.
ALL A are B
NO A is B
SOME A are B
SOME A are NOT B
2 Ninja Technique: The 100/50 Rule
Venn Diagrams take time and can get messy with 3 or 4 statements. Elite candidates use the Income-Expense (100/50) Trick to solve syllogisms in 10 seconds without drawing a single circle.
Step 1: Assign Values (Income)
Every word in a STATEMENT generates 'income'. Memorize this matrix:
| Type | Value Assigned | Pos/Neg |
|---|---|---|
| ALL A are B | A = 100, B = 50 | + Positive |
| NO A is B | A = 100, B = 100 | - Negative |
| SOME A are B | A = 50, B = 50 | + Positive |
| SOME A are NOT B | A = 50, B = 100 | - Negative |
Step 2: Check Viability (Expense)
Treat the CONCLUSION as your 'expense'. Apply these two golden rules:
- The Polarity Rule:
Positive Statement ➡ Positive Conclusion ONLY.
Negative Statement ➡ Negative Conclusion ONLY.
Pos + Neg Statement combined ➡ Negative Conclusion. - The Budget Rule:
If a word earns 50 in the statement, it CANNOT spend 100 in the conclusion.
If a word earns 100, it can spend 100 OR 50.
3 The UPSC Trap Dictionary
The "ONLY" Reverse Trap
When a statement says:
"Only Principals are Teachers."
Decode it as: "ALL Teachers are Principals."
"ONLY A FEW" (The Double Meaning)
This is the most frequent trap in recent exams.
"Only a few Files are approved."
Decode it as a DOUBLE statement:
1. Some Files are approved. (Positive)
AND
2. Some Files are NOT approved. (Negative)
The "EITHER / OR" Complementary Pairs
If you mark both conclusions as "False", before you select "Neither I nor II follows", check if they form an Either/Or pair. Three conditions must be met:
- 1. Both individual conclusions must be technically False (Cannot be determined).
- 2. Both conclusions must have the EXACT SAME subject and object (e.g., Teachers & Budgets).
- 3. They must form one of these pairs: (Some + No) OR (All + Some Not).
4 Admin Context (Solving with 100/50 Rule)
Statements:
1. All Teachers (100) are Graduates (50). [+ Pos]
2. Some Graduates (50) are Administrators (50). [+ Pos]
Conclusions:
I. All Administrators (100) are Teachers (50).
❌ FALSE. Logic: To connect Administrators to Teachers, we need to merge Statement 1 and 2. The common word is 'Graduates'. But 'Graduates' earns only 50 in BOTH statements. To merge, the common word must earn 100 in at least one statement. No connection is possible!
II. Some Administrators (50) are Graduates (50).
✅ TRUE. Logic: This is a direct reverse of Statement 2. Statement 2 is Positive, Conclusion II is Positive. 'Administrators' earns 50 and spends 50. 'Graduates' earns 50 and spends 50. Budget passed!