Syllogism Possibility Rules: The Short Answer
The main syllogism possibility rule is simple: a possibility conclusion such as "All A can be B" or "Some A being B is a possibility" follows whenever it does not contradict anything that is definitely true from the statements. If at least one valid Venn diagram makes it true, it follows. If every valid diagram makes it false, it does not follow.
🔥 Key Exam Takeaway: For a possibility conclusion, do not ask "must this be true?". Ask "can I draw one diagram, without breaking any statement, where this is true?" If yes, it follows. Only a definite fact (a "No", a "Some not", or a chain that forces one) can kill a possibility.
Possibility questions appear in almost every IBPS Clerk, SBI Clerk, IBPS PO and SBI PO prelims syllogism set, usually mixed with definite conclusions and the either-or case. Every rule, table row and answer on this page was checked by brute force: a Python script listed every possible Venn diagram for the statements and tested each conclusion against all of them.
What Is Possibility in Syllogism?
A definite conclusion ("Some A are B") must be true in every diagram that fits the statements. A possibility conclusion only needs to be true in at least one such diagram.
Exams write possibility conclusions in a few standard ways. They all mean the same thing:
| How the conclusion is written | Meaning |
|---|---|
| All A can be B | It is possible that every A is a B |
| Some A can be B | It is possible that at least one A is a B |
| All A being B is a possibility | Same as "All A can be B" |
| Some A being B is a possibility | Same as "Some A can be B" |
| Some A are not B is a possibility | It is possible that at least one A is outside B |
| No A is B is a possibility | It is possible that A and B share nothing |
Possibility words in syllogism to look for
The possibility words are: can be, may be, is a possibility, being ... is a possibility, and chance. Words like at least some, definitely or plain "are" make the conclusion definite, not a possibility.
Definite vs possibility: one quick example
Statement: Some cups are plates.
- "All cups are plates" (definite): does not follow, because we can draw a diagram where some cups are outside plates.
- "All cups can be plates" (possibility): follows, because we can also draw a diagram where all cups are inside plates, and the statement is still true.
Syllogism Possibility Rules Table (Two Terms)
This is the core possibility rules table for syllogism. Learn it once and most questions become look-ups. "T" means the possibility follows; "F" means it does not.
| Given statement | Possibility conclusion | Follows? | Reason |
|---|---|---|---|
| All A are B | All B can be A | T | A and B can be the same set |
| All A are B | Some B are not A is a possibility | T | B can be bigger than A |
| All A are B | Some A can be B | T | It is already definite, so it is also possible |
| All A are B | Some A are not B is a possibility | F | Every A is in B, no exception |
| All A are B | No A is B is a possibility | F | Contradicts "All A are B" |
| Some A are B | All A can be B | T | No statement stops it |
| Some A are B | All B can be A | T | No statement stops it |
| Some A are B | Some A are not B is a possibility | T | A part of A can sit outside B |
| Some A are B | No A is B is a possibility | F | At least one A is in B |
| No A is B | Some A can be B | F | Contradicts "No" |
| No A is B | All A can be B / All B can be A | F | Contradicts "No" |
| Some A are not B | All A can be B | F | At least one A is outside B |
| Some A are not B | No A is B is a possibility | T | Not ruled out |
| Some A are not B | All B can be A | T | B can sit fully inside A |
| Only a few A are B | All A can be B | F | "Only a few" means some A are not B |
| Only a few A are B | No A is B is a possibility | F | "Only a few" also means some A are B |
| Only a few A are B | All B can be A | T | B can sit fully inside A |
Note: A conclusion that is definitely true also counts as a true possibility in IBPS and SBI papers. If "Some A are B" is certain, then "Some A can be B" follows too.
For more on "only a few", see our note on Syllogism Only a Few Rules.
Syllogism Possibility Rules for Chains (Three Terms)
Most questions use two or three statements, so you need to know what happens between the end terms (A and C) of a chain. All rows below were verified against every valid Venn diagram.
| Statements | All A can be C | No A is C possible | All C can be A | Key definite fact |
|---|---|---|---|---|
| All A are B, All B are C | T (already definite) | F | T | All A are C |
| Some A are B, Some B are C | T | T | T | None between A and C |
| All A are B, Some B are C | T | T | T | None between A and C |
| Some A are B, All B are C | T | F | T | Some A are C |
| Some A are B, No B is C | F | T | T | Some A are not C |
| All A are B, No B is C | F | T (definite) | F | No A is C |
| No A is B, All B are C | T | T | F | Some C are not A |
| No A is B, No B is C | T | T | T | None between A and C |
| Only a few A are B, All B are C | T | F | T | Some A are C |
The two traps that decide most possibility questions
Trap 1: "Some A are B, No B is C". Here "Some A are not C" is definite (the A's that are B can never be C). So "All A can be C" is false, but "Some A can be C" and "All C can be A" are both true. Students often mark "All C can be A" wrong; it is not.
Trap 2: "No A is B, All B are C". Here "Some C are not A" is definite (the C's that are B). So "All C can be A" is false, but "All A can be C" is true. The direction matters.
How to Solve Syllogism Possibility Questions (Step-by-Step Trick)
- Draw the minimum diagram. Draw only what the statements force. Keep "Some" overlaps small and leave every other relation open.
- Mark the hard walls. Every "No" is a wall between two circles. Every "Some not" and "only a few" means part of a circle must stay outside another.
- Read the conclusion and try to make it true. Stretch or move circles, but never cross a wall and never remove a forced overlap.
- If you can make it true, it follows. If any wall or forced overlap stops you, it does not follow.
- Check the direction. "All A can be C" and "All C can be A" are different questions. Test each one separately.
The negative-link shortcut
When a chain has a "No" in it, find the circle that is "No" with C. Every term that has a definite overlap with that circle has a part that can never be C. So:
- "All X can be C" is false for any X that definitely overlaps the blocked circle.
- "Some X can be C" is still true unless X is fully inside the blocked circle (or X itself is "No" with C).
Syllogism Possibility Questions with Answers (Solved Examples)
All answers below were confirmed by checking every valid Venn diagram.
Example 1 (IBPS Clerk style)
Statements: Some pens are books. All books are bags. Conclusions: I. All pens can be bags. II. All bags can be pens.
Solution: Some pens are books, so some pens are bags (definite). Nothing stops the rest of the pens from going into bags, so I follows. Nothing stops bags from fitting inside pens either, so II follows. Answer: Both I and II follow.
Example 2 (SBI Clerk style)
Statements: All cars are buses. No bus is a van. Conclusions: I. Some cars can be vans. II. All vans can be buses.
Solution: Cars are inside buses, and buses have a wall with vans. So no car can be a van: I fails. "All vans can be buses" directly contradicts "No bus is a van": II fails. Answer: Neither I nor II follows.
Example 3 (Trap 1 in action)
Statements: Some teas are milks. No milk is sugar. Conclusions: I. All teas can be sugars. II. Some teas can be sugars.
Solution: The teas that are milk can never be sugar, so "Some teas are not sugars" is definite and I fails. The other teas are free, so II follows. Answer: Only II follows.
Example 4 (IBPS PO style, four terms)
Statements: All reds are blues. Some blues are greens. No green is pink. Conclusions: I. All reds can be greens. II. Some pinks can be blues. III. All pinks can be reds.
Solution: Reds have no definite link with greens, so I follows. Pink is only blocked from green; it can overlap the non-green part of blue, so II follows. Reds do not have to touch green, so pinks can sit inside reds: III follows. Answer: All of I, II and III follow.
Example 5 (only a few)
Statements: Only a few golds are silvers. All silvers are irons. Conclusions: I. All golds can be irons. II. All golds can be silvers. III. Some irons are golds.
Solution: Some golds are silvers, so some golds are irons: III is definite. The golds outside silver can still be inside iron, so I follows. "Only a few" means some golds are not silvers, so II fails. Answer: Only I and III follow.
Example 6 (Trap 2 in action)
Statements: No rose is a lily. All lilies are lotuses. Conclusions: I. All lotuses can be roses. II. Some roses can be lotuses. III. All roses can be lotuses.
Solution: The lotuses that are lilies can never be roses, so I fails. Roses only have a wall with lilies, so they can sit in the non-lily part of lotus: II and III follow. Answer: Only II and III follow.
Syllogism Possibility Rules vs Either-Or Case
Do not mix the two ideas:
| Point | Possibility case | Either-or case |
|---|---|---|
| Conclusion wording | "can be", "is a possibility" | Plain definite conclusions |
| What you check | Is it true in at least one diagram? | Neither follows alone, but exactly one is always true |
| Typical pair | Not needed | Some + No, All + Some not |
If both conclusions are plain definite statements and neither follows alone, then check the Syllogism Either-Or Case Rules. A possibility conclusion is judged on its own and never needs a pair.
Common Mistakes in Syllogism Possibility Questions
- Treating "can be" as "is". "All A can be B" does not need to be certain. It only needs to be possible.
- Ignoring direction. In "No A is B, All B are C", "All A can be C" is true but "All C can be A" is false.
- Forgetting the hidden "Some not". "Only a few A are B" and "Some A are B, No B is C" both create a definite "Some A are not ..." that kills an "All A can be ..." conclusion.
- Marking a definite truth as "not a possibility". If something is definitely true, it is also possible.
- Overdrawing. Drawing extra overlaps that the statements do not force makes you miss valid possibilities. Draw the minimum.
Quick Revision Table: Syllogism Possibility Rules
| If the statements give... | Then this possibility is FALSE | Everything else between those terms is |
|---|---|---|
| No A is B | Any "A can be B" / "B can be A" | Usually true |
| All A are B | "Some A are not B" / "No A is B" | True |
| Some A are B | "No A is B" | True |
| Some A are not B | "All A can be B" | True |
| Only a few A are B | "All A can be B" and "No A is B" | True |
| Some A are B, No B is C | "All A can be C" | True |
| No A is B, All B are C | "All C can be A" | True |
| All A are B, No B is C | "Some A can be C", "All C can be A" | No A is C is definite |
Syllogism Possibility Practice Questions with Answers
Options for each: (a) Only I follows (b) Only II follows (c) Either I or II follows (d) Neither I nor II follows (e) Both I and II follow. All answers verified by brute force over every Venn case.
Q1. Statements: All desks are chairs. Some chairs are sofas. Conclusions: I. All sofas can be desks. II. No desk is a sofa is a possibility. Answer: (e) Both follow. Desks have no definite link with sofas, so both a full overlap and no overlap are possible.
Q2. Statements: No dog is a cat. Some cats are cows. Conclusions: I. All cows can be dogs. II. All dogs can be cows. Answer: (b) Only II follows. The cows that are cats can never be dogs, so I fails. Dogs can sit in the non-cat part of cows.
Q3. Statements: All trees are leaves. No leaf is a root. Conclusions: I. Some trees can be roots. II. All roots can be leaves. Answer: (d) Neither follows. Trees are inside leaves, which are walled off from roots.
Q4. Statements: Some inks are pens. Some pens are nibs. Conclusions: I. All inks can be nibs. II. No ink is a nib is a possibility. Answer: (e) Both follow. Two "Some" statements give no definite link between ink and nib, so both possibilities are open. (This is not an either-or case, because possibility conclusions are judged one by one.)
Q5. Statements: Only a few coins are notes. No note is a card. Conclusions: I. All coins can be cards. II. Some coins can be cards. Answer: (b) Only II follows. The coins that are notes can never be cards, so I fails. The coins outside notes are free.
Q6. Statements: All suns are stars. All stars are moons. Conclusions: I. All moons can be suns. II. Some suns are not moons is a possibility. Answer: (a) Only I follows. "All suns are moons" is definite, so II fails. All three sets can be equal, so I follows.
Q7. Statements: Some bats are balls. All balls are nets. No net is a stump. Conclusions: I. Some bats can be stumps. II. All bats can be stumps. III. All stumps can be bats. Answer: Only I and III follow. The bats that are balls are nets and can never be stumps, so II fails. The rest of bat is free, and stumps can sit in the non-net part of bat.
Q8. Statements: Some salts are sands. All salts are soils. Conclusions: I. All soils can be sands. II. No sand is a soil is a possibility. Answer: (a) Only I follows. The sands that are salts are soils, so "Some sands are soils" is definite and II fails.
Q9. Statements: Some A are not B. All B are C. Conclusions: I. All A can be B. II. All A can be C. Answer: (b) Only II follows. "Some A are not B" directly blocks I. A can still sit fully inside C (C is bigger than B).
Q10. Statements: Only a few boats are ships. Only a few ships are yachts. Conclusions: I. All boats can be yachts. II. All ships can be yachts. Answer: (a) Only I follows. "Only a few ships are yachts" means some ships are not yachts, so II fails. Boats and yachts have no definite link, so I follows.
Syllogism Possibility FAQs
What are the possibility rules in syllogism?
A possibility conclusion follows if it can be true in at least one Venn diagram that obeys all the statements. It fails only when a definite fact (a "No", a "Some not", "only a few", or a chain that forces one of these) contradicts it.
How do you know if a possibility follows in syllogism?
Try to draw one diagram where the conclusion is true without breaking any statement. If you can, it follows. If every attempt crosses a "No" wall or removes a forced overlap, it does not.
If a conclusion is definitely true, does its possibility also follow?
Yes. In IBPS and SBI style questions, a definite truth is also a valid possibility. If "All A are B" is certain, "All A can be B" and "Some A can be B" both follow.
What is the difference between "Some A can be B" and "Some A are B"?
"Some A are B" must be true in every valid diagram. "Some A can be B" only needs one valid diagram where it is true. So the second one follows far more often.
Can "All A can be B" follow if only "Some A are B" is given?
Yes. "Some A are B" does not say anything about the rest of A, so all of A can be inside B.
Do possibility conclusions make an either-or case?
No. The either-or case is only for two definite conclusions that form a complementary pair. Each possibility conclusion is judged on its own.
Which exams ask syllogism possibility questions?
IBPS Clerk, SBI Clerk, IBPS PO, SBI PO, IBPS RRB and RBI Assistant prelims ask them regularly. SSC CGL and CHSL ask simpler "can be" conclusions too.
Practice Next
- New tests with syllogism questions: RRB NTPC Syllogism Mock Test 02 and RRB ALP Reasoning Mock Test 01.
- New SSC CGL tests (Tier 1 level): SSC CGL Reasoning Sectional Mock Test 11 and SSC CGL Reasoning Mini Mock Test 04.
- Take the free IBPS Clerk Reasoning Ability Sectional Mock Test 01 and SBI Clerk Reasoning Ability Sectional Mock Test 02 to apply these rules under time.
- More syllogism practice: SSC CGL Syllogism Free Practice Mock Test 2026.
- New topic-wise test: IBPS PO Syllogism Mock Test 01: Possibility and Either-Or Questions with Venn Solutions (15 Questions).
- SBI Clerk level drill: SBI Clerk Syllogism Mock Test 01 (two and three statement questions with possibility cases).
- Related notes: Syllogism Either-Or Case Rules, Syllogism Only a Few Rules, Coded Inequality Tricks, Circular Seating Arrangement Tricks and data sufficiency questions for bank exams, plus Venn diagram questions for SSC CGL.
- Preparing for the bank exam season? See SBI Clerk Recruitment 2026 (Junior Associate).
- Browse all study notes on BookOfExams Notes.