Reasoning

Syllogisms Guide & Practice

Understand Syllogism Venn Diagram representations, categorical statements (Some/All/No), solved exam questions, and online tests. Explore dynamic solver blueprints, master fundamental equations, examine step-by-step solved examples, and practice with real exam-grade mock test sets.

Featured in:SSC CGLSSC CHSLIBPS POIBPS Clerk

Practice Question Papers

Practice Filters

Reasoning

Syllogism - Set 4 Practice Test

Jun 2026Taken by 1 student
25 Qs
37 min
Easy
Reasoning

Syllogism - Set 5 Practice Test

Jun 2026No attempts yet
25 Qs
37 min
Hard
Reasoning

Syllogism - Set 4 Practice Test

Jun 2026No attempts yet
25 Qs
37 min
Hard
Reasoning

Syllogism - Set 2 Practice Test

Jun 2026No attempts yet
25 Qs
37 min
Hard
PrevPage 2 of 2Next
Video Tutorial

Syllogisms Short Tricks & Formulas

Watch this short trick video explaining high-speed shortcuts, mental math formulas, and patterns for Syllogisms. Master the theory and start practicing with the tests below.

Foundation & Concepts

Syllogism is a form of deductive reasoning where a conclusion is drawn from two or more given propositions (premises).

1. Parts of a Proposition

Standard form: Quantifier + Subject + Copula + Predicate

  • Quantifier: Specifies quantity (All, No, Some).
  • Subject: The word about which something is said.
  • Predicate: What is affirmed or denied about the subject.
  • Copula: Relationship between subject and predicate (is, are, are not).

2. Four-fold Classification (A, E, I, O)

SymbolPropositionQuantityQualityVenn Diagram Hint
AAll A are BUniversalAffirmativeA is entirely inside B
ENo A is BUniversalNegativeA and B are disjoint
ISome A are BParticularAffirmativeA and B overlap
OSome A are not BParticularNegativePart of A is outside B

Patterns/Rules

1. Immediate Inferences (Single Statement)

  • All A are B (A) → Implies: Some A are B; Converts to: Some B are A.
  • No A is B (E) → Implies: Some A are not B; Converts to: No B is A.
  • Some A are B (I) → Converts to: Some B are A.
  • Some A are not B (O) → No definite immediate inference.

2. Mediate Inferences (Two+ Statements)

  • Positive + Positive = Positive Conclusion.
  • Positive + Negative = Negative Conclusion.
  • Negative + Negative = No definite conclusion.
  • Particular + Particular = No definite conclusion.
  • Alignment: The "Middle Term" (term common to both premises) must be distributed at least once.

3. Complementary Pairs (Either-Or Case)

"Either I or II follows" applies when:

  1. Both individual conclusions are false/uncertain.
  2. The subject and predicate are the same in both.
  3. They form a pair: (I + O), (A + O), or (I + E).

4. Possibility

  • If no definite relation exists between two terms, any "Possibility" between them is True.
  • If a definite relation exists, a contradicting "Possibility" is False.

Typical Exam Weightage

ExamTypical Questions
SSC (CGL / CHSL / MTS)1–2 questions
Banking (IBPS / SBI)3–5 questions

One of the highest-weightage Banking reasoning topics — the Venn-diagram method is faster and more reliable than verbal elimination for complex statement sets.

Figures are typical ranges based on recent-year patterns, not a guarantee for any specific upcoming paper — always cross-check against the latest official syllabus and previous-year papers for Syllogisms.

Solved Examples

1Solved Example
Easy

Q1. Statements:

  1. All gardens are schools.
  2. All schools are colleges. Conclusions: I. All gardens are colleges. II. Some gardens are colleges.
View Detailed Solution & Explanation
Step-by-Step Explanation

(A + A = A). All gardens -> Schools -> Colleges. Both follow.

  • Answer: Both I and II follow.

Q2. Statements:

  1. Some cups are spoons.
  2. Some spoons are saucers. Conclusions: I. Some cups are saucers. II. No cup is saucer.
  • Solution: Both premises are Particular (I). No definite relation between cups and saucers. However, since they form an (I + E) pair with the same terms, "Either/Or" applies.
  • Answer: Either I or II follows.
2Solved Example
Moderate

Q3. Statements:

  1. Some boys are students.
  2. All students are teenagers. Conclusions: I. All teenagers are students. II. Some boys are teenagers.
View Detailed Solution & Explanation
Step-by-Step Explanation
  • I: "All teenagers are students" is the reverse of A-type, not necessarily true.
    • II: Some boys (who are students) must be teenagers.
  • Answer: Only II follows.

Q4. Statements:

  1. All Lotus are flowers.
  2. No Lily is a Lotus. Conclusions: I. No Lily is a flower. II. Some Lilies are flowers.
  • Solution: Lily is excluded from Lotus, but not necessarily from the entire "flower" category. Lily could overlap with the "flower" area outside "Lotus".
  • Answer: Either I or II follows (Complementary pair E+I).
3Solved Example
Hard

Q5. Statements:

  1. Some birds are trees.
  2. Some trees are hens. Conclusions: I. Some birds being hens is a possibility. II. All trees being hens is a possibility.
View Detailed Solution & Explanation
Step-by-Step Explanation
  • I: No direct relation between birds and hens, so possibility is true.
    • II: "Some trees are hens" allows for the possibility that all trees are hens.
  • Answer: Both I and II follow.

Q6. Statements:

  1. Only Post-graduates are officers.
  2. All officers are sincere. Conclusions: I. Some sincere people are Post-graduates. II. All Post-graduates are sincere.
  • Solution: "Only A are B" means "All B are A". So, "All officers are Post-graduates".
    • Since All officers are sincere and All officers are Post-graduates, they overlap. I follows.
    • II is not necessarily true as there could be Post-graduates who are not officers and thus not necessarily sincere.
  • Answer: Only I follows.