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Syllogism · either–or

Either or syllogism — when “either I or II follows”, with verified practice

An either or syllogism case is answered “Either I or II follows” when three checks all pass: neither conclusion follows on its own, both conclusions have the same subject and the same predicate, and together they form a complementary pair — “Some A are B” with “No A are B”, or “All A are B” with “Some A are not B”.

The either-or option turns up in almost every bank-exam syllogism set, and it is the option candidates most often pick wrongly in both directions — marking it when the pair is not complementary, and missing it when they stop after finding that neither conclusion follows. The full syllogism method covers the definite and possibility cases this page builds on.

How to apply the either or syllogism condition in three checks

  1. Test each conclusion on its own first

    Either-or is only ever considered when neither conclusion follows by itself. If one of them is definite, the answer is “only I” or “only II” (or “both”), and the pair question never arises.

  2. Check that the subject and predicate match

    Both conclusions must talk about the same two terms in the same roles: “Some pens are books” and “No pens are books” qualify. A conclusion about pens and a conclusion about chairs can never form an either-or pair.

  3. Check that the pair is complementary

    Only two pairings count: “Some A are B” with “No A are B”, and “All A are B” with “Some A are not B”. In each pair exactly one is true in every case, so between them they must cover every possibility.

  4. Only then mark “either I or II follows”

    When all three checks pass, the statements do not fix which conclusion is true, but one of them must be. That is precisely what “either I or II follows” claims. If any check fails, the answer is “neither”.

Which conclusion pairs make an either or case

Which conclusion pairs make an either or case
Conclusion pair (neither follows alone)Answer
Some A are B · No A are BEither I or II follows
All A are B · Some A are not BEither I or II follows
Some A are B · Some A are not BNeither — both can be true together
All A are B · No A are BNeither — both can be false together
Some A are B · No A are CNeither — the predicates differ

Practise either or syllogism right now

Every question below was generated by the same engine that mints the DeducePuzzles daily puzzle, and machine-proven to have exactly one correct answer before it reached this page. The walkthrough is the engine's own, step for step.

Question 1

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: No bananas are apples. All apples are oranges.

Conclusion I: No oranges are bananas.

Conclusion II: Some oranges are bananas.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("No oranges are bananas") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("Some oranges are bananas") need not follow — the statements allow a situation where it is false.
  3. Conclusions I and II are a complementary pair — exactly one must be true in every case, but the statements do not fix which. So either I or II follows.

Question 2

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: No jasmines are orchids. Some orchids are marigolds.

Conclusion I: All jasmines are marigolds.

Conclusion II: Some jasmines are not marigolds.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("All jasmines are marigolds") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("Some jasmines are not marigolds") need not follow — the statements allow a situation where it is false.
  3. Conclusions I and II are a complementary pair — exactly one must be true in every case, but the statements do not fix which. So either I or II follows.

Question 3

Take the two statements to be true even if they differ from commonly known facts, then decide which conclusion logically follows.

Statements: No dogs are pets. Some pets are birds.

Conclusion I: All dogs are birds.

Conclusion II: Some dogs are not birds.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either conclusion I or II follows
  4. Neither conclusion I nor II follows
  5. Both conclusions I and II follow
Show the worked solution
  1. Conclusion I ("All dogs are birds") need not follow — the statements allow a situation where it is false.
  2. Conclusion II ("Some dogs are not birds") need not follow — the statements allow a situation where it is false.
  3. Conclusions I and II are a complementary pair — exactly one must be true in every case, but the statements do not fix which. So either I or II follows.
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Common mistakes

Stopping once neither conclusion follows

“Neither follows” is the first check, not the answer. Before you mark “neither”, look at the pair: if the two conclusions are a complementary Some/No or All/Some-not pair, the answer is either-or.

Treating “some are” and “some are not” as opposites

“Some A are B” and “Some A are not B” are both true whenever A is partly inside B, so they are not complementary. They never make an either-or case, however opposite they sound.

Applying either-or when one conclusion already follows

If “Some A are B” is definite, the answer is that conclusion alone, even though its partner “No A are B” makes a textbook pair. Either-or is only for the case where the statements leave both open.

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FAQ

What is the either-or condition in syllogism?

It is the rule for answering “Either I or II follows”: neither conclusion follows on its own, both use the same subject and predicate, and the two form a complementary pair — Some/No or All/Some-not — so exactly one of them must be true in every possible case.

Why is “some A are B” and “some A are not B” not an either-or pair?

Because both can be true at once — whenever A is partly inside B — and an either-or pair needs exactly one of the two to be true in every case. Since neither is forced and they are not complementary, the answer is “neither follows”.

Can either-or apply to possibility conclusions?

Not in the standard bank-exam keys. The either-or rule is taught for the definite pairs Some/No and All/Some-not. A possibility conclusion is judged on its own: it follows if at least one diagram allows it.

Is the either-or rule the same in inequality questions?

The idea is the same — two conclusions about one pair that are each unproven but together cover every case. In inequality the classic trigger is a given A ≥ B with conclusions A > B and A = B.

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