Q1. Statements: 1. All gardens are schools. 2. All schools are colleges. Conclusions: I. All gardens are colleges. II. Some gardens are colleges.

- (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.

Q3. Statements: 1. Some boys are students. 2. All students are teenagers. Conclusions: I. All teenagers are students. II. Some boys are teenagers.

- - 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).

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...

- - 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.

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.

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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)

Symbol	Proposition	Quantity	Quality	Venn Diagram Hint
A	All A are B	Universal	Affirmative	A is entirely inside B
E	No A is B	Universal	Negative	A and B are disjoint
I	Some A are B	Particular	Affirmative	A and B overlap
O	Some A are not B	Particular	Negative	Part 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:

Both individual conclusions are false/uncertain.
The subject and predicate are the same in both.
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

Exam	Typical 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:

All gardens are schools.
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:

Some cups are spoons.
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:

Some boys are students.
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:

All Lotus are flowers.
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:

Some birds are trees.
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:

Only Post-graduates are officers.
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.