Syllogism

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Syllogism is a form of logical reasoning where two or more premises lead to a conclusion. In SSC CGL Tier 1 and Tier 2, syllogism questions test your ability to deduce conclusions from given statements. Understanding the relationship between categorical propositions is essential.

Types of Categorical Statements:

Statement	Meaning	Symbol
All A are B	A ⊆ B	A is subset of B
No A is B	A ∩ B = ∅	A and B are disjoint
Some A are B	A ∩ B ≠ ∅	Some overlap exists
Some A are not B	Some A ∉ B	At least one A is not B

⚡ SSC CGL Exam Tips:

• “Some” means “at least one” — could be all or just one
• When drawing Venn diagrams, consider all possible overlaps
• Conclusions must follow NECESSARILY from premises
• “Could be true” doesn’t count — must be definitely true
• Learn the standard syllogism rules and valid conclusion patterns

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Understanding Syllogism with Venn Diagrams

Statement Type 1: All A are B Draw two circles where A is completely inside B. Possible conclusions:

• Some A are B (✓)
• Some B are A (✓)
• All B are A (✗)
• Some B are not A (✓, if B is larger than A)

Statement Type 2: No A is B Draw two separate circles with no overlap. Possible conclusions:

• No B is A (✓)
• Some A are not B (✓)
• All A are not B = No A is B (✓)

Statement Type 3: Some A are B Draw overlapping circles. Possible conclusions:

• Some B are A (✓)
• Some A are not B (possible but not definite)
• All A are B (✗)
• No A is B (✗)

Worked Examples:

Example 1: Statements:

1. All cats are animals
2. All animals are living beings Conclusions: I. All cats are living beings II. Some living beings are cats

Using Venn diagram: Cats ⊂ Animals ⊂ Living beings Therefore Cats ⊂ Living beings Both conclusions follow.

Answer: Both I and II follow ✓

Example 2: Statements:

1. Some teachers are students
2. All students are learners Conclusions: I. Some teachers are learners II. All teachers are learners

Analysis: Some teachers ∩ students ≠ ∅ Students ⊆ learners So some teachers (the ones who are students) are also learners. I follows ✓ II doesn’t follow (some teachers might not be students/learners) ✗

Answer: Only I follows ✓

Example 3: Statements:

1. No doctor is a nurse
2. Some nurses are women Conclusions: I. No doctor is a woman II. Some women are not doctors

Analysis: Doctors and Nurses are disjoint sets. Some Nurses are Women → Nurses ∩ Women ≠ ∅ This overlap doesn’t involve Doctors. I: No doctor is a woman — Not necessarily. Doctors could be women. ✗ II: Some women are not doctors — Yes, since some women are nurses (who are not doctors). ✓

Answer: Only II follows ✓

⚠️ SSC CGL Common Mistakes:

1. Assuming “Some” means only some, not all
2. Forgetting that “All A are B” allows for “Some B are not A”
3. Not considering all possible Venn diagram arrangements
4. Treating “Some A are not B” as equivalent to “No A is B”

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage with complex syllogisms and previous year SSC CGL patterns.

Advanced Syllogism Rules:

Rule 1: Contrapositive “All A are B” ↔ “No non-B is A” Example: “All humans are mortal” ↔ “No non-mortal is human”

Rule 2: Conversion “Some A are B” ↔ “Some B are A” “No A is B” ↔ “No B is A” But “All A are B” does NOT convert to “All B are A”

Rule 3: Obversion “All A are B” ↔ “No A is non-B” “Some A are B” ↔ “Some A are not non-B” (trivial)

Rule 4: Subalternation “All A are B” → “Some A is B” (but reverse doesn’t work) “No A is B” → “Some A is not B” (but reverse doesn’t work)

Complementary Pairs: When two conclusions cover all possibilities:

• “Some A are B” and “Some A are not B” — together they cover all A
• In either-or questions, one of the pair must be true

Complement Sets:

• “All A are B” complement is “Some A are not B”
• “No A is B” complement is “Some A are B”
• “Some A are B” complement is “No A is B” (or the possibility of all/no overlap)

Three-Term Syllogisms:

When you have three terms (A, B, C):

Example: Statements:

1. All Indians are Asians
2. All Asians are humans Conclusions: I. All Indians are humans II. Some humans are Indians

Both follow: Indians ⊂ Asians ⊂ Humans Therefore Indians ⊂ Humans ✓

Previous Year SSC CGL Patterns:

SSC CGL 2022: Statements:

1. All roses are flowers
2. No lotus is a rose Conclusions: I. No lotus is a flower II. Some flowers are roses

Analysis:

• Roses ⊂ Flowers
• Lotus ∩ Roses = ∅ I: No lotus is a flower — Not necessarily. Lotuses are flowers in general, but the statement only says no lotus is a ROSE, not that lotuses aren’t flowers in general. The lotus and rose sets are both subsets of flowers and don’t overlap with each other, but lotuses still belong to flowers. Wait: “No lotus is a rose” means lotus set and rose set are disjoint. Both can still be inside flowers. ✓ Actually this DOES mean no lotus is a rose, but lotus IS a type of flower, so no lotus is a rose = true. But the conclusion says “No lotus is a flower” which is wrong. Actually lotus is a type of flower. So conclusion I is false (lotus IS a flower). II: Some flowers are roses — Yes, since roses ⊂ flowers. ✓

SSC CGL 2022: Statements:

1. Some pens are books
2. All books are pages Conclusions: I. Some pens are pages II. All pages are books

I: Pens ∩ books ≠ ∅. Books ⊂ pages. So the intersection of pens and books is also in pages. ✓ II: Books ⊂ pages. Pages could include non-book pages. ✗

Answer: Only I follows ✓

SSC CGL 2023: Statements:

1. All doctors are professionals
2. No professional is unemployed Conclusions: I. No doctor is unemployed II. Some professionals are doctors

Analysis:

• Doctors ⊂ Professionals
• Professionals ∩ Unemployed = ∅ I: Doctors ∩ Unemployed = ∅ (since Doctors ⊂ Professionals) ✓ II: Doctors ⊂ Professionals, so some professionals are doctors (actually all professionals who are doctors). ✓

Both follow ✓

SSC CGL 2023: Statements:

1. Some cars are vehicles
2. No bike is a car Conclusions: I. Some vehicles are bikes II. No bike is a vehicle

Analysis:

• Cars ∩ Vehicles ≠ ∅
• Cars ∩ Bikes = ∅ I: Vehicles ∩ Bikes — Could be. Vehicles include cars, bikes, etc. Some vehicles could be bikes. Not definite. ✗ II: No bike is a vehicle — Also not definite. Bikes are vehicles (generally), but the statement says no bike is a car, not that bikes aren’t vehicles. Wait, “no bike is a car” just means bikes and cars don’t overlap. Bikes could still be vehicles. So II doesn’t follow.

Answer: Neither follows ✗

Possibility Cases in Syllogisms:

When conclusion says “could be” or “might be,” it’s valid if a Venn diagram arrangement exists where it could be true.

Example: Statements:

1. All A are B
2. Some B are C Conclusions: I. Some C are A (could be) II. All C are A (not necessarily)

I is possible but not definite. If conclusion uses “could be,” it follows. If it says “is,” it doesn’t.

Either-Or Cases:

When neither conclusion is definitely true, but one must be true:

• “Some A are B” (not definite) and “Some A are not B” (also not definite) — one might be true depending on actual overlap.

But typically in SSC CGL, “either I or II follows” appears when neither is definitely true.

Immediate Inference Rules:

Premise	Conclusion
All S are P	Some S are P (✓), Some P are S (✓)
No S is P	No P is S (✓), Some S are not P (✓)
Some S are P	Some P are S (✓)
Some S are not P	(No immediate conclusion)

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