Syllogism is the bedrock of formal logic — you are given two or more statements about categories of things, and you must determine which conclusions necessarily follow from those statements, regardless of real-world truth.
Here's the core mental model: treat each statement as a boundary condition on sets. The statements define what is permitted, and your only job is to read those boundaries correctly. You are not checking whether the statements are factually true. If a statement says "All politicians are honest," you accept it. Your job is pure geometry of sets.
Think of it this way — imagine categories as circles on a whiteboard. Each statement tells you how those circles overlap, contain, or exclude each other. A conclusion "follows" only when every possible arrangement of those circles forced by the statements makes that conclusion true. If even one valid arrangement exists where the conclusion fails, the conclusion does not follow.
This is where most candidates slip: they confuse "possible" with "definite." A conclusion that is sometimes true is not the same as one that always must be true. RBI Grade B questions, particularly in the Preliminary exam, frequently exploit this confusion with attractive-looking conclusions that hold in one diagram arrangement but not another.
The four building blocks of every syllogism are:
Almost all RBI Grade B syllogism questions combine three statements and ask you to evaluate three conclusions. The challenge is not the individual deduction — it is the chained deduction across three terms.
Stop drawing elaborate, artistic circles. In the exam hall, draw minimal rough circles — speed matters. Use single letters: P, Q, R for the three categories.
For each statement type, your diagram should reflect the following:
All A are B: Draw circle A completely inside circle B.
Some A are B: Draw circles A and B partially overlapping (intersection exists).
No A are B: Draw circles A and B with no overlap at all — completely separate.
Some A are not B: Circle A is not fully inside B — part of A sits outside B. This can look like a partial overlap or A completely outside B.
In three-statement syllogisms, you need to connect A → B → C to see what you can say about A and C. Here are the definitive combination rules:
Chain 1: All + All = All All A are B. All B are C. → All A are C. (certain)
Chain 2: All + Some = Some (forward only) All A are B. Some B are C. → We cannot conclude "Some A are C." The "some B" that are C may or may not be the part of B that contains A. But: Some A are B. All B are C. → Some A are C. (certain — the overlapping portion moves forward)
Chain 3: All + No = No All A are B. No B are C. → No A are C. (certain)
Chain 4: Some + No = Some Not Some A are B. No B are C. → Some A are not C. (certain)
Chain 5: No + Some = Some Not (reversed) No A are B. Some B are C. → Some C are not A. (certain, but note the reversal)
Chain 6: Some + All = Some (forward) Some A are B. All B are C → Some A are C. Wait — this does work. If some A are B, and every B is inside C, then those "some A" are guaranteed to be inside C too.
This is the most commonly tested chain in RBI Grade B. Internalize it: Some + All = Some.
Sometimes a conclusion is just a restatement of a premise, read from the other direction.
Conversion is a free deduction — you always get it. In RBI PYQs, converted forms of premises appear as conclusions, and many candidates incorrectly reject them.
When a question asks about "either I or II follows," look for complementary pairs. If one conclusion says "Some A are B" and another says "No A are B," they are complementary — exactly one of them must be true. If you cannot determine which, the answer is "either I or II follows."
This is a trap RBI Grade B setters love: both individual conclusions seem uncertain, but together they cover all cases.
Some exam variants include conclusions phrased as "Some A can be B" or "It is possible that some A are B." These require a different test — you just need to check whether any diagram arrangement exists where this could be true, rather than whether it is always true. Check the question wording carefully. If the exam frame says "definite conclusions," ignore possibility conclusions unless they are definitively true.
Remember four output rules using SANO (Some, All, No, Output): — Some + All = Some (output same direction) — All + No = No (output same direction) — Some + No = Some Not (output same direction) — All + All = All (output same direction)
Any chain involving two "Some" statements produces nothing definite.
Standard method (draw diagram + check each conclusion): ~60s per question. Using SANO to pre-identify the single valid chain deduction before drawing: ~25s.
Micro-example: "Some A are B. All B are C." → SANO rule "Some + All = Some" → Some A are C. Done in one step, no diagram needed.
The moment you see a conclusion that looks like a reversed premise, apply the conversion test instantly: — "No A are B" in premise → "No B are A" is a free conclusion (E-type always converts). — "Some A are B" in premise → "Some B are A" is a free conclusion (I-type always converts).
Standard method (re-derive from scratch): 3 steps. Conversion reflex: 1 step — you recognize it as a flipped premise and mark it true immediately.
Micro-example: Premise says "No harmful substances are beneficial." Conclusion says "Some beneficial things are not harmful." This is NOT a direct conversion — do not accept it automatically. But "No beneficial things are harmful" would be a valid E-conversion. Know the difference.
When the link between two categories is "Some A are B" (not "All"), any conclusion about the full set of A based on what is true for B is blocked.
Rule: If the connecting statement is "Some," you can only conclude "Some" — never "All" and never "No."
Use this to eliminate wrong conclusions in under 5 seconds: — If a conclusion says "No A are C" but the A-to-B link is "Some A are B," eliminate that conclusion immediately without drawing anything. — If a conclusion says "All A are C" but any link in the chain is "Some," eliminate it.
Step count: Standard (draw diagram, test conclusion) = 4 steps. Elimination rule = 1 step.
In a three-statement problem, identify which statement uses "All" or "No" — that is your anchor. Draw that circle relationship first, then fit the "Some" statement around it.
This prevents the common error of starting with the weakest link and drawing an incorrect diagram.
Speed gain: Candidates who start with "Some" often redraw their diagram 1-2 times (losing ~30s). Starting with the "All" or "No" statement produces the correct base diagram on the first attempt.
Micro-example: Statements — "No A are B. Some B are C. All C are D." Start with "No A are B" (strong separation), then place C overlapping B, then place D containing all of C. Single-draw, no correction needed.
Before solving any conclusion set, scan for complementary pairs: one conclusion says "Some A are B" and another says "No A are B" (or "All A are B" vs "Some A are not B"). These pairs are exhaustive — one must be true.
If neither follows definitively from the statements, the answer is "either I or II follows" (if the question allows it).
Standard method (evaluate both conclusions individually): 2 full derivations = ~50s. Complementary pair detection: identify the pair in ~5s, and if both are uncertain, answer immediately.
When you see a syllogism question in the exam hall, move through this decision tree:
Step 1 — Count and label. How many statements? Two or three? Label categories A, B, C.
Step 2 — Identify statement types. Mark each as All/Some/No. Circle any "All" and "No" — these are your strong anchors.
Step 3 — Check for direct conversions. Can any conclusion be read as a converted premise? If yes, mark it true immediately.
Step 4 — Apply SANO chain rules. For each pair of adjacent statements, apply the formula: Some+All=Some, All+No=No, Some+No=Some-Not. If a chain gives a definite result, mark matching conclusions true.
Step 5 — Use the Partial Overlap Blocker. Any conclusion saying "All" or "No" about a category connected only by "Some" — eliminate it.
Step 6 — Draw only if uncertain. If Steps 3-5 have not resolved all conclusions, draw a minimal Venn diagram. Use rough circles, not precision art.
Step 7 — Check for complementary pairs among the remaining uncertain conclusions before committing.
Target time per syllogism question: under 90 seconds.
Why this question: This is the cleanest example of the Some+All=Some chain and its limits — understanding exactly when a chain fires and when it does not determines the entire answer.
Solving path:
Conclusion I: "Some phones are useful" — Apply SANO: Some P are S, All S are U → Some+All=Some → Some P are U. Follows.
Conclusion II: "Some smart things are not waste" — All S are U (so S is inside U). No U are W. So no S are W. This means "No smart things are waste" is definite. "Some smart things are not waste" is weaker than "No smart things are waste" — a weaker conclusion of a definite truth always holds. Follows.
Conclusion III: "No phones are waste" — Only "some" phones are smart (not all). The remaining phones have no established connection to "useful" or "waste." No definite conclusion about all phones. Does not follow.
Answer: Only I and II follow.
Why this question: This question tests the critical distinction — "All rivers are water" means rivers are inside the water circle, but the "Some water is clean" does not tell you which part of water overlaps with rivers.
Solving path:
Conclusion I: "Some rivers are clean" — The clean portion of water could be entirely outside the rivers portion. No guarantee. Does not follow.
Conclusion II: "Some water is not polluted" — Some W are C, and no C are W... wait — no C are P. Since some W are C, and no C are P, those "some W" are not P. So some water is not polluted. Follows.
Conclusion III: "No rivers are polluted" — We cannot connect rivers to clean (as shown above), so we cannot chain rivers through clean to "not polluted." Does not follow.
Answer: Only II follows.
Why this question: Same structural pattern as the previous question but with different vocabulary — this tests whether you recognize the pattern across domains, not just memorize a specific answer.
Solving path:
Conclusion I: "Some medicines are harmful" — The harmful portion of drugs could be entirely outside the medicines portion. Not guaranteed. Does not follow.
Conclusion II: "Some drugs are not beneficial" — Some D are H, and no H are B. Those "some D" are H, and since no H are B, those "some D" are not B. Follows.
Conclusion III: "No medicines are beneficial" — We cannot connect all medicines to harmful, so we cannot conclude all medicines fall outside beneficial. Does not follow.
Answer: Only II follows.
Why this question: This question from a later set introduces "No executive is complacent" — a negative universal starter — and tests whether you carry the chain correctly without smuggling in an unwarranted deduction about executives.
Solving path:
Conclusion II: "Some demotivated people are complacent" — Some C are U, all U are D → Some+All = Some → some C are D. By conversion (I-type), some D are C. Follows.
Conclusion I: "No executive is unsuccessful" — E and C are separate. But U overlaps with C, not necessarily with E. Executives could be unsuccessful for reasons entirely unrelated to complacency. Does not follow.
Conclusion III: "All executives are motivated" — We know executives are not complacent, but we cannot infer their motivation status from this. The path E → C → U → D does not connect since E and C are separate. Does not follow.
Answer: Only conclusion II follows.
Why this question: This question tests whether you correctly apply the chain through a "No flowers are trees" starting point and track what follows about green things.
Solving path:
Conclusion III: "Some trees are green" — Some T are P, all P are G → Some+All=Some → some T are G. Follows.
Conclusion I: "Some green are trees" — From above, some T are G. By I-type conversion, some G are T. Follows.
Conclusion II: "No flowers are plants" — We know F and T are separate. But P overlaps with T — the overlapping portion of P that is T is separate from F, yes. However, P could also extend beyond T, into a region that does overlap with F. No statement rules this out. Does not follow.
Answer: Only I and III follow.
Accepting "All A are B" as "All B are A." This is the single most common conversion error. "All smart things are useful" does not mean "All useful things are smart." A-type (universal affirmative) converts only to I-type ("Some B are A"), not back to A-type.
Confusing the direction of "Some + All" chains. "All A are B, some B are C" does not give you "some A are C." The chain only works when "Some" comes first: "Some A are B, All B are C → Some A are C." The "some B" that are C may be entirely outside the "all A" region.
Marking a conclusion false because it sounds real-world implausible. "All politicians are honest" is a statement you must accept. Syllogism is pure set logic. Real-world truth is irrelevant.
Missing I-type conversion as a free deduction. "Some A are B" in a premise automatically gives you "Some B are A" as a valid conclusion. Many candidates spend time re-deriving this when it is instant.
Accepting "Some A are not C" when the chain gives "No A are C." "No A are C" is stronger, and "Some A are not C" follows from it automatically. But watch for the reverse error: you cannot go from "Some A are not C" to "No A are C."
Ignoring the "possible conclusion" vs "definite conclusion" distinction. If the question asks for definite conclusions, any conclusion that holds in some diagrams but not all must be rejected. If it asks for possible conclusions, the test is whether any valid arrangement supports it.