Welcome to the comprehensive, textbook-style guide on Syllogism for the IBPS PO (Probationary Officer) Prelims examination. Syllogism is one of the highest-yield topics in the Reasoning Ability section, accounting for 3 to 5 marks in almost every shift of the prelims exam. Master standard categorical propositions, conversion rules, the 150-100 (Income-Expenditure) method, possibility rules, and complementary pairs to solve these questions accurately in under two minutes.
1. Exam Pattern & Weightage Analysis
In recent IBPS PO Prelims shifts, Syllogism questions follow distinct modern patterns including "Only a few", "Some not", and direct Possibility conclusions. Analyzing Previous Year Questions (PYQs) reveals:
- Weightage: 3–5 Questions per prelims shift.
- Target Time: Less than 25–30 seconds per question using direct rules or Venn Diagrams.
- Question Formats: Direct conclusions, Reverse Syllogism (rare in Prelims, common in Mains), and Either-Or cases.
2. Standard Categorical Propositions
A categorical proposition states a relation between two terms: a Subject (\(A\)) and a Predicate (\(B\)). There are four fundamental standard categorical propositions utilized in deductive reasoning:
| Type | Classification | Statement Form | Set Notation / Meaning |
|---|---|---|---|
| A | Universal Affirmative | All \(A\) are \(B\) | \(A \subseteq B\) |
| E | Universal Negative | No \(A\) are \(B\) | \(A \cap B = \emptyset\) |
| I | Particular Affirmative | Some \(A\) are \(B\) | \(A \cap B eq \emptyset\) |
| O | Particular Negative | Some \(A\) are not \(B\) | \(A \setminus B eq \emptyset\) |
3. Conversion Rules
Conversion involves interchanging the Subject and Predicate terms without altering the logical truth value of the proposition:
- A \(\to\) I: "All \(A\) are \(B\)" converts validly to "Some \(B\) are \(A\)".
- E \(\to\) E: "No \(A\) are \(B\)" converts validly to "No \(B\) are \(A\)".
- I \(\to\) I: "Some \(A\) are \(B\)" converts validly to "Some \(B\) are \(A\)".
- O \(\to\) No Conversion: "Some \(A\) are not \(B\)" yields no valid logical conversion.
4. The 150-100 (Income & Expenditure) Method
The 150-100 method allows candidate to solve syllogisms rapidly without drawing Venn diagrams by evaluating numerical values assigned to Subjects and Predicates.
Value Assignment Rules
- Universal Affirmative (A): Subject = \(100\), Predicate = \(50\)
- Universal Negative (E): Subject = \(100\), Predicate = \(100\)
- Particular Affirmative (I): Subject = \(50\), Predicate = \(50\)
- Particular Negative (O): Subject = \(50\), Predicate = \(100\)
Income & Expenditure Execution Rules
- Positive Statement (\(+\)): Predicate takes a value of \(50\).
- Negative Statement (\(-\)): Predicate takes a value of \(100\).
- Universal Statements: Subject takes a value of \(100\).
- Particular Statements: Subject takes a value of \(50\).
Golden Rule: Treat the values in the statements as Income and the values in the conclusions as Expenditure. If an item's income is \(50\), its expenditure cannot be \(100\). Furthermore, positive statements only yield positive conclusions, while negative statements yield negative conclusions.
5. Handling Possibility Cases
Possibility conclusions require checking whether a statement contradicts established definite relations:
- Definite Truth Rule: If a relation is 100% definitely true in real terms, its possibility is logically False.
- Doubtful Case Rule: If there is no direct relationship or definite information given between two terms (doubtful scenario), its possibility is logically True.
- Universal Possibility: "All \(A\) are \(B\) is a possibility" is Valid as long as \(A\) and \(B\) do not explicitly contradict each other in the given premises.
6. Either-Or (\(\lor\)) Complementary Pair Rules
An "Either-Or" scenario arises when two individual conclusions cannot be definitively proven true independently, but together cover all logical conditions.
Conditions for Either-Or
- Both conclusions must individually be false/doubtful.
- Both conclusions must contain the exact same Subject and Predicate.
- The conclusions must form a valid complementary pair.
Valid Complementary Pairs
- A + O: All + Some Not
- I + E: Some + No
- I + O: Some + Some Not
Critical Exception: The pair A + E ("All" + "No") does NOT form an Either-Or pair because both statements can simultaneously be false when terms partially overlap.
7. People Also Ask (Frequently Asked Questions)
Q1: Can 'All + No' form an Either-Or case in IBPS PO Syllogism?
Answer: No. The 'All + No' (A + E) pair is not a complementary pair because both can be false simultaneously if the actual relation is 'Some'.
Q2: How do you solve 'Only a few' Syllogism questions in IBPS PO?
Answer: 'Only a few A are B' contains two hidden relations: 'Some A are B' (positive) AND 'Some A are not B' (negative). Both conditions must be satisfied simultaneously.
Q3: What is the 150-100 method in Syllogism?
Answer: The 150-100 method assigns numerical income values (100 for universal, 50 for particular) to subjects and predicates. Conclusions are validated by ensuring expenditure does not exceed statement income.
Boost Your IBPS PO Preparation!
Get daily practice sets, 1 Lakh+ PYQs, and high-yield study notes on our official Telegram channel.
Join Telegram Channel