Syllogisms: Step-by-Step Rules and 8 Worked Examples

Syllogisms appear in TCS NQT, AMCAT, CoCubes, and Infosys SP aptitude tests, and the question format is always the same: two premises, one conclusion, one answer asking whether the conclusion follows.

The reasoning chain is fixed. Premise 1 states something about two terms. Premise 2 adds a statement about one of those terms and a third term. The conclusion proposes a relationship between the first and third. Your job is to verify that relationship using only what the premises say, nothing more, nothing less.

Where syllogisms appear in placement tests

Syllogisms appear in the logical reasoning sections of AMCAT, TCS NQT, CoCubes, eLitmus, and company-specific aptitude rounds. The Infosys campus placement process treats reasoning ability as a standalone section; syllogisms are one of its five topic types alongside blood relations, coding-decoding, statement-conclusion, and data sufficiency.

A typical placement-round logical reasoning block has 15 to 20 questions, and syllogisms account for 2 to 4 of them. Most students have 45 to 90 seconds per question. Getting the Venn diagram method right once means the same technique works across all test platforms.

The reasoning skill is the same as in blood relation questions: given stated relationships, derive an unstated one. In blood relations you build a family tree. In syllogisms, you draw overlapping circles.

The three syllogism types

Placement tests draw from three syllogism types. The method for solving each is slightly different.

Categorical syllogism

The most common type. Statements classify objects into categories using ‘All’, ‘Some’, or ‘No’. The middle term appears in both premises and links the subject to the predicate.

• Statement 1: All dogs are mammals.
• Statement 2: All mammals are animals.
• Conclusion: All dogs are animals.
• Valid: Yes. Every dog is inside the mammal circle, and every mammal is inside the animal circle, so every dog is inside the animal circle.

Hypothetical syllogism

Uses ‘If…then’ conditions. The conclusion follows when Premise 2 satisfies the ‘if’ condition stated in Premise 1.

• Statement 1: If it rains, the ground will be wet.
• Statement 2: It is raining.
• Conclusion: The ground is wet.
• Valid: Yes. Premise 2 triggers the condition stated in Premise 1.

Disjunctive syllogism

Uses ‘Either…or’ choices. Eliminating one option forces the other.

• Statement 1: Either the bus is late or I missed it.
• Statement 2: The bus is not late.
• Conclusion: I missed the bus.
• Valid: Yes. One option is eliminated by Premise 2, so the other must hold.

Five deduction rules

These five rules apply to categorical syllogisms, which make up the majority of placement-test questions. Apply them before reaching for a Venn diagram; two of the rules let you discard a question before drawing anything.

Rule	Premise condition	Valid conclusion
1	Both affirmative (‘All’ or ‘Some’)	Conclusion may be affirmative
2	One premise negative	Conclusion must be negative
3	Both premises negative	No valid conclusion
4	Both premises particular (‘Some’)	No universal conclusion possible
5	One premise particular (‘Some’)	Conclusion is particular, not universal

Rule 3 is the fastest filter in a timed test. Scan both premises first. If both say ‘No’ or ‘not’, move on without reading the conclusion.

Rule 5 is where most students lose marks. ‘All A are B’ paired with ‘Some B are C’ cannot produce ‘All A are C’. It produces at most ‘Some A are C’, and only when the A’s overlap with the C’s through B. When the rules alone do not settle the question, use the Venn diagram method below.

The Venn diagram method

Three steps work for any categorical syllogism.

1. Draw three overlapping circles, one per term. Label them A (subject), B (middle term), C (predicate). The middle term is the one that appears in both premises.
2. Fill in each circle per its premise statement:
   • ‘All A are B’: draw the A circle entirely inside the B circle.
   • ‘Some A are B’: mark the overlapping region (at least one shared member).
   • ‘No A are B’: draw the circles completely separate with no overlap.
3. Test the conclusion: check whether the conclusion is true in every valid diagram. If yes, it follows. If any valid diagram makes the conclusion false, the answer is ‘Cannot be determined’ or ‘Does not follow’.

The phrase ‘necessarily true’ is the key distinction. A conclusion that holds in some configurations but not all is ‘Cannot be determined’, not ‘True’. This is the source of the most common mistake in placement tests.

Eight worked examples

The eight examples below cover all three types and include the most common placement-test variants. Every answer is re-derived from first principles.

Categorical (All-All): transitivity holds

• Q1. Statement 1: All apples are fruits. Statement 2: All fruits are healthy.
• Conclusion: All apples are healthy.
• Rule check: Both affirmative and universal. Rule 1 permits an affirmative conclusion.
• Venn: Apple circle inside fruit circle, fruit circle inside healthy circle. Apple circle is therefore inside healthy circle.
• Answer: True.

Categorical (All-Some): middle-term uncertainty

• Q2. Statement 1: All birds are animals. Statement 2: Some animals can fly.
• Conclusion: Some birds can fly.
• Rule check: Rule 5 applies (second premise particular). The flying animals may or may not include birds.
• Venn: Bird circle inside animal circle. Mark a region inside animal circle for ‘can fly’. That region may overlap with birds or may not. Both configurations satisfy the premises.
• Answer: Cannot be determined.

Categorical (All-No): excluded category

• Q3. Statement 1: All cats are animals. Statement 2: No animals are plants.
• Conclusion: No cats are plants.
• Rule check: One negative premise. Rule 2: conclusion must be negative.
• Venn: Cat circle inside animal circle. Animal and plant circles are completely separate. Cat circle is therefore completely separate from plant circle.
• Answer: True.

Categorical (No-All): partial exclusion

• Q4. Statement 1: No birds are cats. Statement 2: All cats are mammals.
• Conclusion: Some mammals are not birds.
• Rule check: One negative premise. Conclusion must be negative (Rule 2). Cat circle is inside mammal circle. Bird and cat circles are completely separate. At least the cats inside the mammal circle are not birds.
• Answer: True.

Categorical (Some-Some): double uncertainty

• Q5. Statement 1: Some students are girls. Statement 2: Some girls are intelligent.
• Conclusion: Some students are intelligent.
• Rule check: Both premises particular (Rule 4). No definite conclusion is possible.
• Venn: Two configurations exist: one where student-girls and intelligent-girls overlap, and one where they do not. Both satisfy the premises.
• Answer: Cannot be determined.

Categorical (All-Some, reversed): white flowers

• Q6. Statement 1: All roses are flowers. Statement 2: Some flowers are white.
• Conclusion: Some roses are white.
• Rule check: Rule 5 (second premise particular). White flowers may or may not include roses.
• Venn: Rose circle inside flower circle. Mark a region inside flower circle for ‘white’. That region may or may not overlap with roses. Both configurations satisfy the premises.
• Answer: Cannot be determined.

Hypothetical: affirming the consequent

• Q7. Statement 1: If it rains, the ground will be wet. Statement 2: The ground is wet.
• Conclusion: It has rained.
• Rule check: Hypothetical syllogism. Premise 2 asserts the consequent, not the antecedent. The ground can be wet for reasons other than rain.
• Answer: Cannot be determined. Affirming the consequent does not validate the antecedent.

Disjunctive: one option eliminated

• Q8. Statement 1: Either the power fails or the server crashes. Statement 2: The server did not crash.
• Conclusion: The power failed.
• Rule check: Disjunctive syllogism. Premise 2 eliminates one option, forcing the other.
• Answer: True.

Three common mistakes in placement tests

Confusing ‘Cannot be determined’ with ‘False’

‘Cannot be determined’ means the conclusion is neither necessarily true nor necessarily false: two valid Venn configurations exist, one where the conclusion holds and one where it does not. ‘False’ means the conclusion is definitely wrong given the premises. Picking ‘False’ when the correct answer is ‘Cannot be determined’ is the single most frequent error in syllogism questions.

Assuming information not given in the premises

Placement syllogisms are closed systems. No outside knowledge applies. ‘All birds are animals / Some animals can fly’ does not let you use your knowledge that sparrows or eagles fly. Only what the premises state explicitly is available.

Misreading ‘Some’ as ‘All’

‘Some A are B’ states only that at least one A is a B. It does not imply all A are B, and it does not imply ‘Some B are A’ is false. The moment a conclusion requires more than that minimum overlap, it overreaches the premise.

For number analogy questions in the same test block, the analogous error is applying a pattern that seems to fit one pair but skipping verification on the second pair. State the rule, verify both halves, then apply.

---

The same discipline from the Venn diagram method, stating which rule applies before drawing any inference, translates directly to prompting language models effectively. Structured prompting follows the same logic: state the constraint, verify the output satisfies it, iterate. TinkerLLM is an LLM environment at ₹299 where engineering students practise this kind of step-by-step reasoning with actual models.