Syllogism is the art of drawing conclusions from a set of given statements using pure logic — not your real-world knowledge, not common sense, and definitely not what you "know" about cars, dogs, or guitars. You are being tested on whether you can follow the rules of logical deduction, period.
Here is the core idea: you are given two or three statements (called premises) and two or three conclusions. Your job is to identify which conclusions must be true if the statements are accepted as true — even if those statements sound bizarre in real life. "All cats are dogs" is a perfectly valid statement for a syllogism question. Don't argue with it. Work with it.
Think of syllogism like a relay race. Statement I passes the baton to Statement II. If they are connected through a shared term, you can derive a new conclusion. If they are not connected, no baton exchange happens, and no conclusion follows.
The typical question format in UP Police Constable: two or three statements, followed by two conclusions, followed by four options like "Only Conclusion I follows / Only Conclusion II follows / Both follow / Neither follows." You need to pick the right one.
Three types of statements you will always see:
The Venn diagram picture in your head is the single most reliable tool here. Before you read the conclusions, draw the circles — mentally or on your rough sheet. Let the picture decide, not your gut.
| Code | Statement Form | Picture | | ---- | --------------- | -------------------------------- | | A | All X are Y | X circle completely inside Y | | E | No X is Y | X and Y circles completely apart | | I | Some X are Y | X and Y circles overlap | | O | Some X are not Y| Part of X is outside Y |
This is the most tested rule in UP Police syllogism. Conversion means flipping subject and predicate.
Look — the most common mistake in UP Police papers is accepting "All Y are X" as a valid conversion of "All X are Y." It is not. If all cats are animals, that does not mean all animals are cats.
When two statements share a common middle term, you can link them into one conclusion. The quality of the conclusion depends on the weakest link:
| Statement I | Statement II | Conclusion | | ----------- | ------------ | ---------- | | All A are B | All B are C | All A are C | | All A are B | Some B are C | Some A are C | | Some A are B| All B are C | Some A are C | | All A are B | No B is C | No A is C | | Some A are B| No B is C | Some A are not C | | Some A are B| Some B are C | No definite conclusion |
The last row is critical: Some + Some = Nothing. You cannot chain two particular statements.
If one statement is negative, the conclusion (if it exists) must be negative. If both statements are negative, no conclusion follows.
When one statement is particular (Some) and one is universal (All / No):
When there are three statements, work in pairs. Take Statement I + II first, derive an intermediate conclusion. Then combine that intermediate conclusion with Statement III to get your final conclusion. Draw the Venn as you go — three overlapping circles, filled in step by step.
Sometimes neither conclusion independently follows, but together they form a complementary pair — one saying "Some X are Y" and the other saying "Some X are not Y." In such cases, the answer is "either I or II follows." This is a special case. UP Police questions occasionally use this, so keep it in mind.
Syllogism questions in the exam are sometimes camouflaged as "Statement and Conclusion" questions with real-world scenarios (cricket matches, players, etc.). In those cases, the logic is the same — does the conclusion necessarily follow, or is it merely possible or probable? If it is only probable, it does not follow. Stick to what the statements definitively say.
Map the four statement types to a mental traffic light before reading any conclusion. A (All) = Green full go, E (No) = Red full stop, I (Some) = Yellow partial overlap, O (Some not) = Yellow partial gap. When you see two Greens in the chain, expect a Green conclusion. One Yellow + one Green = Yellow conclusion. One Red anywhere = Red conclusion. This mental mapping takes 3 seconds versus drawing full Venn diagrams (15-20 seconds) for straightforward two-statement questions.
Before accepting any conclusion, ask: "Is this the original statement, the valid conversion, or the converse trap?" Valid conversions: All→Some (flip), No→No (flip), Some→Some (flip). The trap: All→All (flip) is always wrong. Test every conclusion against this three-second flip check. Standard approach of drawing Venn for each conclusion: ~20 seconds per conclusion. Flip test: ~5 seconds. Saves 15 seconds per conclusion on average.
When both statements are particular (both start with "Some"), the answer for any chain conclusion is automatically "No conclusion / Neither follows." Do not waste time drawing Venn diagrams. Identify "Some...Some" pattern, mark "no chain conclusion possible," move on. This eliminates one trap answer in about 2 seconds versus spending 30 seconds drawing diagrams only to reach the same answer.
"All A are B" + "No B is C" always gives "No A is C." This is a guaranteed, direct conclusion. Memorise this as the "Full Block" pattern — the All pushes every A into B, and No blocks all of B from C, so every A is blocked from C. Recognition time: 3 seconds. Without this pattern, a student traces through the Venn step by step in about 25 seconds.
When a conclusion sounds "obviously true" from real life (e.g., "all sitars are instruments" sounds logical in real life), immediately flag it as a potential trap. Ask: "Does this follow from the statements, or do I just know it to be true?" If the statement says "All instruments are sitars," real-world knowledge says sitars are a subset of instruments — but logically you must accept the statement as written. Applying this gut-check saves 1-2 wrong answers per paper, which can be the difference in the cut-off.
In the exam hall, follow this exact sequence for every syllogism question:
Step 1 (5 seconds): Read all statements. Identify the type of each — A, E, I, or O. Note the middle term (the term shared between two statements).
Step 2 (5 seconds): Apply Some+Some check. If both statements are particular, mark "no conclusion" and move on.
Step 3 (10 seconds): Draw a quick Venn diagram for valid chains. Use the chain rules above to derive what the combined statements say.
Step 4 (5 seconds per conclusion): Check each given conclusion against your Venn diagram. Does the conclusion match exactly, or is it a forbidden conversion?
Step 5 (3 seconds): Check for the complementary pair trap — if conclusions are "Some X are Y" and "Some X are not Y," answer "either-or."
Decision rule for "definitely true" vs "probably true" questions: Only accept a conclusion if it is 100% forced by the statements. "Probably" and "possibly" are not enough. If the Venn picture allows the conclusion to be false in even one valid arrangement, it does not follow.
Target: complete each syllogism question in under 40 seconds.
Why this question: Tests the conversion rule — the most common trap in UP Police syllogism. Students who accept "All trucks are cars" as a valid inference lose marks here.
Solving path: Statement I: "Some cars are bikes" — draw overlapping circles for cars and bikes. Statement II: "No bike is a truck" — trucks circle is completely separate from bikes. Conclusion I: "All trucks are cars" — look at your diagram. Trucks are only confirmed to be outside bikes. Nothing connects trucks to cars. Rejected. Conclusion II: "Some bikes are cars" — this is the valid conversion of "Some cars are bikes" (I ↔ Some). Accepted. Answer: Only Conclusion II follows.
Why this question: Tests the All+All chain rule and the forbidden All-conversion trap. Two universal affirmatives appear, and students must resist reversing the final conclusion.
Solving path: Statement I: All pets are dogs (pets circle fully inside dogs). Statement II: All dogs are cats (dogs circle fully inside cats). Chain: pets → dogs → cats, so All pets are cats. Conclusion I follows. Conclusion II: All cats are pets — this would require the chain to run backwards (cats → pets), which is a forbidden All-conversion. A separate group of cats can exist outside pets. Rejected. Answer: Only Conclusion I follows.
Why this question: Tests All+All chain again but now the conclusion that "sounds" true (All sitars are instruments) is actually the trap — it is the real-world truth but not a logical deduction from these statements.
Solving path: Statement 1: All guitars are instruments (guitars inside instruments). Statement 2: All instruments are sitars (instruments inside sitars). Chain: guitars → instruments → sitars, so All guitars are sitars. Conclusion 2 follows. Conclusion 1: All sitars are instruments — this reverses Statement 2. Your gut says yes because in real life instruments include sitars, but the statement says the opposite. Logically, by these statements, sitars is the larger set. The conversion of "All instruments are sitars" is only "Some sitars are instruments," not "All sitars are instruments." Rejected. Answer: Only Conclusion 2 follows.
Why this question: Three-statement chain. Tests whether you can trace Some → All → All correctly and correctly reject the reverse chain.
Solving path: Statement I: Some pumpkins are beetroots. Statement II: All beetroots are garlic. Chain I+II: Some pumpkins are garlic (Some + All = Some). Conclusion I follows. Now Statement II + III: All beetroots are garlic + All garlic are turnips → All beetroots are turnips. Conclusion III follows. Conclusion II: All garlic are pumpkins — to get this, you would need all garlic to be traced back to pumpkins. But only "some pumpkins" connected to garlic via beetroots. The garlic circle is large; only a portion overlaps with pumpkins. Rejected. Answer: Only Conclusions I and III follow.
Why this question: Tests the All+No = No chain (the "Full Block" pattern). One of the cleanest chain deductions in syllogism.
Solving path: Statement I: All pizzas are toppings (pizzas fully inside toppings). Statement II: No topping is tasty (toppings and tasty circles completely apart). Chain: All pizzas are toppings + No topping is tasty → No pizza is tasty. Every pizza is in the toppings group, and the toppings group has zero overlap with tasty. So zero pizzas can be tasty. Conclusion II follows. Conclusion I (All pizzas are tasty) directly contradicts this — Rejected. Answer: Only Conclusion II follows.
Why this question: Tests whether you can resist drawing conclusions from statistical data. This is the "real-world scenario" syllogism variant that UP Police occasionally uses.
Solving path: The statements say spinners scored 60 out of 120 runs. Conclusion 1 claims 20% of the team are spinners — but runs scored says nothing about the number of players. Conclusion 2 claims middle-order batsmen were spinners — batting position is never mentioned. Both conclusions import information not present in the statements. Answer: Neither conclusion follows.
Why this question: A clean two-statement deduction where the conclusion is certain. Tests whether you correctly follow the logical chain without second-guessing.
Solving path: Statement 1: Tray plays table tennis. Statement 2: Table tennis is a difficult game. Substituting: Tray plays [a difficult game]. The middle term "table tennis" connects both statements and drops out, leaving the conclusion intact. This is a straightforward chain with no ambiguity. The conclusion is definitely true.
Accepting "All Y are X" as the conversion of "All X are Y." This is the single most common error. "All instruments are sitars" does not convert to "All sitars are instruments." The valid conversion is only "Some sitars are instruments." Every time you see an "All" conclusion, verify it came from a chain, not from a flip.
Using real-world knowledge instead of the given statements. If the statement says "All sitars are instruments," the logical world of this question puts sitars as the bigger set — regardless of what you know about music. Work only with what the statements say.
Chaining two "Some" statements. Some A are B + Some B are C gives no conclusion about A and C. Many students draw overlapping circles and assume the overlap "must extend" — it does not have to. The answer is always "no conclusion" for a Some+Some chain.
Missing the complementary pair option. When one conclusion says "Some X are Y" and the other says "Some X are not Y," and neither independently follows, the correct answer is "either I or II follows" — not "neither follows." Missing this costs you the mark.
Treating "probably" as "definitely." In conditional or real-scenario questions (like the cricket/player question), "probably true" does not count. If the conclusion can be false even while the statements remain true, it does not follow.
Ignoring the direction of the chain. "All A are B" means A is inside B — not B is inside A. When you draw Venn diagrams, always put the subject inside the predicate for "All" statements. Getting the direction wrong invalidates every subsequent step.