Syllogism asks you to decide whether a conclusion definitely follows from given statements, regardless of what the real world says. In AFCAT Reasoning and Military Aptitude it is one of the most scoring verbal areas because the rules are fixed and patterns repeat. Draw circles, test every arrangement, and accept only what is always true in every diagram.
What syllogism really tests
A syllogism gives you two or more premises (statements you must accept as true) and one or more conclusions. Your only job is to check whether each conclusion necessarily follows from the premises using logic alone, never your general knowledge.
The trap is real-world bias. A premise may say All pens are tables. It does not matter that this is false in reality — for the question, pens are tables, and you reason from there. Many bright candidates lose easy marks only because they keep arguing “but that is not true in real life”. In logic the truth of the premise is assumed; you are graded purely on whether the conclusion is forced by those exact words.
Each AFCAT paper usually carries three to five syllogism questions, and they are set so a trained candidate finishes fast while an untrained one second-guesses and wastes time. Because the rules never change from year to year, syllogism is among the highest return-on-effort topics in the entire Reasoning and Military Aptitude section. A few hours of focused drilling converts almost every such question into a confident, quick tick.
Accept every premise as 100% true. A conclusion is valid only if it holds in every possible diagram you can draw — not just one convenient picture.
The four standard statement types
Almost every syllogism is built from four quantifier types. Learn how each maps to circles, because the picture decides the answer.
- All A are B (Universal Positive): circle A lies completely inside circle B.
- No A is B (Universal Negative): circles A and B are fully separate, touching nowhere.
- Some A are B (Particular Positive): circles A and B overlap in at least one part.
- Some A are not B (Particular Negative): part of A lies outside B; the rest may or may not overlap.
A useful habit is to label each premise the moment you read it: write a small tag such as “All+”, “No−”, “Some+” or “Some−” beside it. This instantly tells you which combining rule applies and warns you when both premises are particular or both negative, where a definite conclusion is usually impossible.
All A are B never means All B are A. Inside the big circle B there can be plenty of B that are not A. Reversing “All” blindly is the single biggest error.
Distribution: the key to valid links
Behind the friendly circle method sits one formal idea: distribution. A term is “distributed” when the statement talks about all members of that term.
- In All A are B, the subject A is distributed; B is not.
- In No A is B, both A and B are distributed.
- In Some A are B, neither term is distributed.
- In Some A are not B, only the predicate B is distributed.
Two practical laws follow. First, the middle term (the common term linking the premises) must be distributed in at least one premise, or nothing combines. Second, a term distributed in the conclusion must already be distributed in its premise. These two checks alone catch most wrong options without any drawing, and they are the formal reason the combining rules below work.
If the common term is “Some” in both premises, it is never distributed, so no definite conclusion can link the end terms. Spot this and reject universal conclusions instantly.
Conversion: free conclusions hidden in premises
Every premise hides a guaranteed conclusion called its conversion. Knowing these saves time because the answer is often just a converted premise.
- All A are B → Some B are A (always true). It does NOT give All B are A.
- No A is B → No B is A (always true, fully symmetric).
- Some A are B → Some B are A (always true, symmetric).
- Some A are not B → gives nothing certain in reverse; “Some B are not A” does not follow.
Before drawing anything, write the conversion of each premise in the margin. In many AFCAT questions one printed conclusion is simply a conversion — an instant tick that needs no diagram at all.
The circle (Venn-diagram) method, step by step
The fastest reliable approach is to draw a valid arrangement first, then test conclusions against alternatives.
- Convert each premise into circles exactly as the four types demand.
- Combine all premises into one diagram, keeping every given relation true.
- Read each conclusion. If it is true in this diagram, try to draw a second valid diagram where it becomes false.
- If you can break it, the conclusion does not follow. If it survives every arrangement, it follows.
The whole skill lies in step 3. Most wrong answers are conclusions that happen to be true in the first diagram a candidate draws but can be made false in a second, equally legal diagram. Treat every conclusion as guilty until you have failed to disprove it.
Drawing only one diagram and stopping. A conclusion that “looks true” in one picture but can be made false in another does not follow. Always attempt to disprove it.
Quick rules for combining two premises
For two-statement sets, these shortcut rules from the standard reasoning framework cover most cases and let you skip drawing in clean situations.
- All + All = All. All A are B, All B are C → All A are C.
- All + No = No. All A are B, No B is C → No A is C.
- Some + All = Some. Some A are B, All B are C → Some A are C.
- Some + No = Some-not. Some A are B, No B is C → Some A are not C.
- No + No, Some + Some, Some-not + anything = no definite conclusion.
If both premises are particular (Some) or both negative (No), you usually get nothing certain. The middle term must be distributed for a clean link, exactly as the distribution rule predicts.
The either-or case
Sometimes two conclusions are each individually uncertain, yet together they cover all possibilities. Then the answer is Either I or II follows. Two conditions must both hold:
- Both conclusions are individually invalid (neither follows on its own), AND
- They share the same subject and predicate but are of opposite type — one positive and one negative, e.g. Some A are B versus No A is B, or All A are B versus Some A are not B.
If both conclusions are individually invalid, do not rush to mark “neither follows”. First run the either-or pair test — AFCAT loves slipping in one such case to catch hasty candidates.
Possibility conclusions
Modern papers add conclusions worded as “Some A being B is a possibility” or “All A being C is a possibility”. These flip the logic, so handle them with care.
- A possibility conclusion follows if you can draw at least one valid diagram in which it is true.
- It fails only if the premises make it impossible in every diagram.
For definite conclusions you hunt for a diagram that breaks them. For possibility conclusions you hunt for a single diagram that supports them. The mindset is exactly reversed.
Example: if the premise is No A is B, then “Some A being B is a possibility” is false, because no legal diagram allows any A–B overlap. But “All cats being animals is a possibility” is true whenever nothing forbids that overlap.
Three or more statements
AFCAT often gives three premises and two or three conclusions. The method does not change: build one combined diagram honouring every premise, then test each conclusion against all valid arrangements. The trick is to resolve the set in pairs, chaining through the common terms.
Example: All cats are dogs; All dogs are mammals; No mammal is a fish. Chain it: All cats are dogs + All dogs are mammals ⇒ All cats are mammals. Then All cats are mammals + No mammal is fish ⇒ No cat is fish. Each link uses one clean rule, and a long chain is just several two-statement deductions stacked together.
Testing each conclusion against only the two nearest premises. A conclusion may involve non-adjacent terms; always read it against the full combined picture before deciding.
Worked example
Statements: (1) All pilots are officers. (2) Some officers are graduates. Conclusions: I. Some pilots are graduates. II. Some graduates are officers.
Answer: Only Conclusion II follows.
Conclusion II was just a conversion of premise 2. Spotting conversions first would have answered the question with almost no drawing.
Speed shortcuts for the exam
Syllogism is a place to bank quick marks. Train these reflexes until they become automatic.
- First scan conclusions for any conversion of a premise — mark it valid instantly.
- If both premises contain Some, a definite positive conclusion is rarely valid — expect “does not follow”.
- For two opposite, individually-invalid conclusions on the same terms, check either-or before deciding.
- For possibility wording, ask only “can I draw it once?” — usually yes unless a premise forbids it.
- Spend no more than 40–50 seconds per set; draw lightly and move on.
The correct answer must be true under all diagrams for definite conclusions, and under at least one diagram for possibility conclusions.
Previous-year style question and recap
Q. Statements: (1) All aircraft are machines. (2) No machine is living. Conclusions: I. No aircraft is living. II. Some machines are aircraft. Which conclusion(s) follow?
Answer: Both I and II follow. All aircraft are machines + No machine is living gives All + No = No, so “No aircraft is living” (I) follows. “All aircraft are machines” converts to “Some machines are aircraft” (II), which is always true.
- Accept premises as true; ignore real-world facts.
- Map All / No / Some / Some-not into circles.
- Conversions: All→Some (reverse), No→No, Some→Some; Some-not gives nothing.
- Two-premise rules: All+All=All, All+No=No, Some+All=Some, Some+No=Some-not.
- Test definite conclusions across all diagrams; possibility needs just one diagram.
- Check either-or when two opposite conclusions are each invalid.