What Is the Either-Or Case in Syllogism? (Quick Answer)
In syllogism, the answer is "Either I or II follows" only when three things are true together: (1) neither conclusion follows on its own (both are doubtful), (2) both conclusions talk about the same two terms, and (3) the two conclusions form a complementary pair, which in IBPS and SBI exams means "Some + No" or "All + Some not". If even one condition fails, the either-or case does not apply, and the answer is usually "Neither I nor II follows".
🔥 Key Exam Takeaway: Check each conclusion on its own first. Only when both come out as "can't say" do you look for a complementary pair. A pair where one conclusion is already definitely true is never an either-or case.
This topic shows up almost every year in the Reasoning section of IBPS Clerk, SBI Clerk, IBPS PO and SBI PO prelims, and also in SSC CGL and CHSL in a simpler form. Usually 1 or 2 questions in a set of 3 to 5 syllogism questions test the either-or idea, so it is worth getting perfectly right.
What Is a Complementary Pair in Syllogism?
A complementary pair is a set of two conclusions about the same two terms where, in every possible Venn diagram for the statements, exactly one of them is true. They can never both be true and never both be false. So even if you cannot say which one is true, you know for sure that one of them is.
| Pair | Conclusion I | Conclusion II | Why exactly one is true |
|---|---|---|---|
| Some + No | Some A are B | No A is B | Either A and B share at least one member, or they share none. There is no third case. |
| All + Some not | All A are B | Some A are not B | Either every A is inside B, or at least one A is outside B. There is no third case. |
These are the two pairs used in current IBPS and SBI papers and taught by the major bank-exam coaching sources. In classical logic they are called contradictory pairs (I and E, A and O).
Which Pairs Are Not Complementary Pairs in Syllogism?
| Looks like a pair | Why it fails | What it usually gives |
|---|---|---|
| All A are B + No A is B | Both can be false together (when some A are B and some are not) | Neither I nor II |
| Some A are B + Some A are not B | Both can be true together (when only part of A is in B) | Treated as not a pair in the current bank pattern |
| Some A are B + Some B are A | They mean the same thing | Both follow or neither follows |
| All A are B + Some B are not A | Terms are crossed, so they are not opposites | Neither I nor II |
Note on "Some + Some not": Some older books list "Some + Some not" as a third complementary pair. Current IBPS/SBI-style questions and most recent bank-exam material use only "Some + No" and "All + Some not", because "Some A are B" and "Some A are not B" can both be true at the same time. Stick to the two-pair rule for bank exams.
Syllogism Either-Or Case Conditions (3 Rules for IBPS and SBI Clerk 2026)
Tick all three before you mark "Either I or II follows".
| Condition | What to check | Quick test |
|---|---|---|
| 1. Both are doubtful | Neither conclusion follows definitely, and neither is definitely false | Draw the basic diagram and one or two possible diagrams. Each conclusion must be true in one diagram and false in another. |
| 2. Same terms | Both conclusions use the same two terms (subject and predicate) | "Some pens are bags" and "No pen is a bag" both talk about pens and bags. |
| 3. Complementary pair | The pair is "Some + No" or "All + Some not" | Match the words in the conclusions with the table above. |
Can the Terms Be Swapped in an Either-Or Case?
- For Some + No, the subject and predicate can be swapped. "Some A are B" means the same as "Some B are A", and "No A is B" means the same as "No B is A". So "Some A are B" and "No B is A" still form a valid pair.
- For All + Some not, the order must be exactly the same. "All A are B" pairs with "Some A are not B" only. "All A are B" with "Some B are not A" is not a pair.
Either-Or vs Neither-Nor Case in Syllogism
"Neither I nor II follows" is the answer when:
- both conclusions are doubtful and they do not form a complementary pair, or
- one or both conclusions are definitely false and the other does not follow.
The most common neither-nor trap is "All + No". When the statements leave the relation between two terms open, "All A are C" and "No A is C" are both doubtful, but they are not opposites, because the real answer could be "some A are C and some are not". So the answer is neither, not either-or.
How to Solve Either-Or Syllogism Questions (Step-by-Step Venn Diagram Trick)
- Draw the basic diagram using only what the statements say. Draw circles as small or as overlapping as allowed, and never add a link the statements do not give.
- Test each conclusion alone. Mark it as True (true in every diagram), False (false in every diagram) or Doubtful (true in some diagrams, false in others). To test, try to draw a diagram that breaks it.
- If any conclusion is True, that conclusion follows. Do not look for either-or with it.
- If two conclusions are both Doubtful, check condition 2 (same terms) and condition 3 (complementary pair).
- All three conditions met: mark "Either I or II follows". Otherwise, mark "Neither I nor II follows".
🔥 Key Exam Takeaway: In new-pattern questions with three conclusions, a common answer is "Only I and either II or III follow". Solve each conclusion separately, then pair up the doubtful ones.
Syllogism Either-Or Case Examples (IBPS and SBI Clerk & PO Pattern)
Every answer below was checked against all possible Venn diagrams.
Example 1: Basic Some + No pair
Statements: Some pens are books. Some books are bags.
Conclusions: I. Some pens are bags. II. No pen is a bag.
Solution: Pens and bags are linked only through books, and the two "some" links need not meet. In one diagram the pen part and the bag part of books overlap, so some pens are bags. In another they do not, so no pen is a bag. Both are doubtful, the terms are the same (pens, bags) and the pair is Some + No.
Answer: Either I or II follows.
Example 2: All + Some not pair
Statements: All cars are buses. Some buses are trains.
Conclusions: I. All trains are cars. II. Some trains are not cars.
Solution: The train circle overlaps the bus circle somewhere. It is possible to draw the train circle fully inside the car circle (then all trains are cars), and it is also possible to draw it outside (then some trains are not cars). Both are doubtful, both have "trains" as subject and "cars" as predicate in the same order, and the pair is All + Some not.
Answer: Either I or II follows.
Example 3: Trap, one conclusion is definite
Statements: Some apples are mangoes. All mangoes are grapes.
Conclusions: I. Some apples are grapes. II. No apple is a grape.
Solution: The apples that are mangoes are also grapes, because all mangoes are grapes. So conclusion I is definitely true and conclusion II is definitely false. Even though "Some + No" is a complementary pair, condition 1 fails.
Answer: Only I follows.
Example 4: Some + No with swapped terms
Statements: Some cups are plates. No plate is a spoon.
Conclusions: I. Some cups are spoons. II. No spoon is a cup.
Solution: Cups and spoons can overlap in the part of cups that is outside plates, or they can stay apart. So both conclusions are doubtful. Conclusion II is "No spoon is a cup", which means the same as "No cup is a spoon". Swapping is allowed for Some + No, so the pair is valid.
Answer: Either I or II follows.
Example 5: Crossed All + Some not (not a pair)
Statements: Some X are Y. All Y are Z.
Conclusions: I. All Z are X. II. Some X are not Z.
Solution: Both are doubtful. But conclusion I has Z as the subject while conclusion II has X as the subject, so the terms are crossed. Both can be false together: draw X fully inside Z, with Z bigger than X. Then not all Z are X, and no X is outside Z.
Answer: Neither I nor II follows.
Example 6: The All + No trap
Statements: Some laptops are phones. No phone is a tablet.
Conclusions: I. All tablets are laptops. II. No tablet is a laptop.
Solution: Tablets are only known to be outside phones. They may be fully inside laptops, partly inside or fully outside. Both conclusions are doubtful, but All + No is not a complementary pair, because "some tablets are laptops and some are not" makes both false.
Answer: Neither I nor II follows.
Example 7: New pattern with three conclusions
Statements: All roses are lilies. No lily is a tulip. Some tulips are daisies.
Conclusions: I. Some daisies are not roses. II. Some roses are daisies. III. No rose is a daisy.
Solution:
- I: The daisies that are tulips cannot be lilies (no lily is a tulip), so they cannot be roses (all roses are lilies). So some daisies are not roses. True.
- II and III: A daisy may also sit inside the rose circle, as long as it is outside tulips. Or roses and daisies may stay apart. Both are doubtful, same terms, Some + No pair.
Answer: Only I and either II or III follow.
Example 8: Both doubtful, same terms, still neither
Statements: Some A are B. Some B are C.
Conclusions: I. All A are C. II. No A is C.
Solution: Same idea as Example 6. The relation between A and C is fully open, but All + No is not a complementary pair.
Answer: Neither I nor II follows.
Common Traps in Syllogism Either-Or Questions
| Trap | Why students fall for it | Correct approach |
|---|---|---|
| Marking either-or when one conclusion is definitely true | They see "Some + No" and jump | Always test each conclusion alone first |
| Treating "All + No" as a pair | They look like opposites | They can both be false. Answer is neither. |
| Crossing terms in "All + Some not" | "All A are B" and "Some B are not A" look similar | Subject and predicate must be in the same order |
| Forgetting that "Some + No" allows swapping | They think the order must match | "Some A are B" + "No B is A" is valid |
| Pairing conclusions about different terms | Same words like "some" and "no" appear | Both conclusions must name the same two terms |
| Using "Some + Some not" | Older books list it | Not used as a pair in the current bank pattern |
| Missing the either-or inside a 3-conclusion question | They stop after finding one true conclusion | Check every remaining pair of doubtful conclusions |
Syllogism Either-Or Rules: Quick Revision Table
| Situation | Answer |
|---|---|
| One conclusion definitely true | That conclusion follows (no either-or) |
| Both doubtful + same terms + Some/No | Either I or II |
| Both doubtful + same terms + All/Some not (same order) | Either I or II |
| Both doubtful + All/No | Neither I nor II |
| Both doubtful + All/Some not with crossed terms | Neither I nor II |
| Both doubtful + different terms | Neither I nor II |
| Both definitely true | Both follow |
Syllogism Either-Or Case Questions with Answers (Practice Set)
Options for each question (unless stated): (a) Only I follows (b) Only II follows (c) Either I or II follows (d) Neither I nor II follows (e) Both follow.
Q1. Statements: All books are pages. Some pages are notes. Conclusions: I. Some books are notes. II. No book is a note.
Q2. Statements: Some boys are girls. All girls are teachers. Conclusions: I. Some boys are teachers. II. No boy is a teacher.
Q3. Statements: All lions are tigers. No tiger is a bear. Conclusions: I. No lion is a bear. II. Some lions are bears.
Q4. Statements: Some reds are blues. Some blues are greens. Conclusions: I. All greens are reds. II. Some greens are not reds.
Q5. Statements: Some keys are locks. No lock is a door. Conclusions: I. Some doors are keys. II. No key is a door.
Q6. Statements: All tables are chairs. Some chairs are sofas. Conclusions: I. All sofas are tables. II. No table is a sofa.
Q7. Statements: Some A are B. All B are C. No C is D. Conclusions: I. Some A are not D. II. Some D are A. III. No A is D. Options: (a) Only I (b) Only I and II (c) Only I and either II or III (d) Either II or III only (e) None follows
Q8. Statements: All pens are inks. All inks are papers. Conclusions: I. All pens are papers. II. Some papers are not pens.
Q9. Statements: Some rivers are lakes. Some lakes are ponds. Conclusions: I. Some rivers are not ponds. II. All rivers are ponds.
Q10. Statements: No car is a bike. Some bikes are cycles. Conclusions: I. Some cycles are not cars. II. Some cars are cycles.
Answers and Explanations
- (c) Books and notes are linked only through pages, so both are doubtful. Same terms, Some + No pair.
- (a) The boys who are girls are teachers, so I is true and II is false.
- (a) Lions are inside tigers and tigers are fully outside bears, so no lion is a bear. II is false.
- (c) Greens and reds are linked only through two "some" links. Both doubtful, same order (greens → reds), All + Some not pair.
- (c) Both doubtful. "Some doors are keys" equals "Some keys are doors", and swapping is allowed for Some + No.
- (d) Both doubtful, but All + No is not a complementary pair.
- (c) The A that are B are inside C, and C is fully outside D, so some A are not D (I true). A and D may overlap outside C or may not, so II and III are doubtful and form a Some + No pair.
- (a) Pens are inside inks, inks inside papers, so all pens are papers. II is doubtful (papers could be exactly the pens), so it does not follow, and no either-or arises because I is already true.
- (c) Rivers and ponds have no fixed link. Both doubtful, same order (rivers → ponds), All + Some not pair.
- (a) The cycles that are bikes cannot be cars, so some cycles are not cars. II is only possible, so it does not follow.
Syllogism Either-Or Case FAQs
What are the rules and conditions for the either-or case in syllogism?
Both conclusions must be doubtful on their own, they must use the same two terms, and they must form a complementary pair: "Some + No" or "All + Some not".
What is a complementary pair in syllogism?
It is a pair of conclusions where exactly one is always true in every possible diagram. In bank exams the two pairs are "Some A are B / No A is B" and "All A are B / Some A are not B".
Is "All + No" a complementary pair?
No. "All A are B" and "No A is B" can both be false at the same time when some A are B and some are not. If both are doubtful, the answer is "Neither I nor II follows".
Is "Some + Some not" an either-or case in bank exams?
Not in the current IBPS and SBI pattern. Both statements can be true together, so most recent bank-exam material does not treat them as a complementary pair, even though some older books do.
Can the subject and predicate be swapped in an either-or case?
Only for the "Some + No" pair, because both "some" and "no" statements can be reversed without changing meaning. For "All + Some not" the order must be exactly the same.
What is the difference between either-or and neither-nor in syllogism?
Either-or means one of the two doubtful conclusions must be true because they are complementary. Neither-nor means none of the conclusions follows and they do not form such a pair.
Can an either-or case come with a "possibility" conclusion?
Rarely. Either-or questions are usually built on ordinary definite-type conclusions. Possibility conclusions ("All A being B is a possibility") are judged on their own as true or false.
Related topics: revise syllogism possibility rules next.
Practice Next: Syllogism and Reasoning Mock Tests
- Learn the next syllogism rule: Syllogism Only a Few Rules with Venn Method
- Take a timed section test: IBPS Clerk Reasoning Ability Sectional Mock Test 01
- More bank-pattern practice: SBI Clerk Reasoning Ability Sectional Mock Test 01
- Same either-or logic in inequality: Coded Inequality Tricks for Bank Exams
- Pure syllogism drill: SSC CGL Syllogism Free Practice Mock Test
- New topic-wise test: IBPS PO Syllogism Mock Test 01: Possibility and Either-Or Questions with Venn Solutions (15 Questions).
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