Syllogism Cheat Sheet and Rules - IBPS PO (Probationary Officer) Prelims

1. Introduction to Syllogism

In competitive examinations like IBPS PO Prelims, Syllogism is a core section within Logical Reasoning. A syllogism is a deductive logical argument where conclusions are derived from two or more given statements or premises. Candidates must assume all given statements to be 100% true, even if they contradict commonly known real-world facts.

• Premise: The given standard statements acting as the foundational data.
• Conclusion: Derived claims that must be validated as Definitely True, Definitely False, or a Possibility.
• Key Components: Every categorical syllogism comprises three essential terms: the Subject, the Predicate, and the Middle Term (which connects both premises).

2. Categorical Propositions (A, E, I, O Types)

Standard logical statements are classified into four distinct categorical propositions based on quality (affirmative/negative) and quantity (universal/particular):

A-Type: Universal Affirmative

Form: All A are B.
Venn Representation: Circle A is completely contained inside Circle B.
Distribution: Subject \(A\) is distributed; Predicate \(B\) is undistributed.

E-Type: Universal Negative

Form: No A are B.
Venn Representation: Circle A and Circle B are completely disjoint with a cross-relation line showing no intersection.
Distribution: Both Subject \(A\) and Predicate \(B\) are distributed.

I-Type: Particular Affirmative

Form: Some A are B.
Venn Representation: Circle A and Circle B intersect partially.
Distribution: Neither Subject \(A\) nor Predicate \(B\) is distributed.

O-Type: Particular Negative

Form: Some A are not B.
Venn Representation: At least a portion of Circle A remains outside Circle B.
Distribution: Predicate \(B\) is distributed; Subject \(A\) is undistributed.

3. Golden Rules of Distribution

A term is said to be distributed in a statement if the statement makes a claim about all members of the class represented by that term.

1. Universal Statements (A, E): These always distribute their Subject terms (e.g., in "All A are B", all members of \(A\) are referenced).
2. Negative Statements (E, O): These always distribute their Predicate terms (e.g., in "No A are B" and "Some A are not B", the predicate \(B\) is fully excluded from the referred subject class).

4. Standard Syllogism Shortcuts & Rules

When combining statements direct conclusions can be evaluated using standard combination rules without drawing Venn diagrams:

• \(A + A \to A\): All A are B + All B are C \(\implies\) All A are C.
• \(A + E \to E\): All A are B + No B are C \(\implies\) No A are C.
• \(I + A \to I\): Some A are B + All B are C \(\implies\) Some A are C.
• \(I + E \to O\): Some A are B + No B are C \(\implies\) Some A are not C.

5. Either-Or Complementary Cases

An 'Either-Or' condition applies when neither individual conclusion can be verified as definitely true on its own, but together they cover all possible logical scenarios (forming a complementary pair).

Conditions required for an Either-Or case:

1. Both conclusions must be individually doubtful/uncertain (neither definitely true nor definitely false).
2. The subject and predicate terms in both conclusions must be identical (or dynamically interchangeable).
3. The pair of conclusions must form one of the standard complementary pairs:
   • Some + No (I + E Pair)
   • All + Some Not (A + O Pair)
   • Some + Some Not (I + O Pair)

6. PYQ Analysis & IBPS PO Pattern

NTA & IBPS Exam Pattern

In the IBPS PO Prelims exam, Logical Reasoning accounts for 35 questions, out of which Syllogisms routinely command 3 to 5 questions. Recent trend analysis shows a shift towards "Only a few" and "Can never be" type statement patterns alongside classic direct combinations.

Chapter Weightage Analysis

People Also Ask (Frequently Asked Questions)