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Either-or (complementary pairs)

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⏱ 5 min read🧩 5 question types🎯 12 practice Q
The idea in one minute

Sometimes neither conclusion follows on its own, but they are exact opposites. Then one of them is true in every picture, and the answer is 'Either I or II follows'.

Only two shapes of pairs qualify. Always test each conclusion alone first.

01

What an either-or pair is

Sometimes neither conclusion follows on its own, but the two conclusions are exact opposites. Then one of them is true in every picture. The answer is Either I or II follows.

This is logic, not luck. If two conclusions are negations of each other, no picture can make both false.

03

The three-step test

  1. Check the pair. Same two terms? One of the two legal shapes? If not, there is no either-or.
  2. Test each conclusion alone. If one follows, the answer is 'Only I' or 'Only II'.
  3. If neither follows alone, the answer is 'Either I or II follows'.

Rule: Always do step 2 before step 3. A conclusion that follows alone rules out either-or.

04

Pairs that look right but are not

  • Different terms. 'All A are B' and 'Some A are not C' are not opposites.
  • No and Some-not. Both can be false. A group inside B has some A in B, but no A outside B.
  • All and No. Both can be false when A partly overlaps B.
  • Some and Some-not. Both can be true together, so exams do not treat them as a pair.

Watch: Two conclusions that are both false at the same time are never an either-or pair.

05

Extra statements

With three statements, ignore the extra one while you check the pair shape. It matters only in step 2, where it may prove one conclusion alone.

06

Where it shows up in the options

The option 'Either I or II follows' appears only when the answer is truly either-or. If you see it, do not pick it by habit.

Check the pair shape and run the alone test before you choose it.

07

Why the pairs work

Take 'All A are B' and 'Some A are not B'. A is either entirely inside B or not. There is no third case.

Take 'Some A are B' and 'No A are B'. The two groups either share a member or they share none. Again there is no third case.

08

A worked example

Statements

  • All keys are metals.

Conclusions

  • I. Some keys are iron.
  • II. No keys are iron.

Options

  • (A) Either I or II follows
  • (B) Neither I nor II follows
  • (C) Only I follows
  • (D) Only II follows

Solution

  • Same two terms: keys and iron. The pair is 'Some' and 'No'.
  • The statement does not link keys to iron, so neither follows alone.
  • Keys and iron either share a member or do not. One of the two is always true.

Answer: (A) Either I or II follows.

09

Question types you will see

Each type: how to recognise it, the method step by step, and one question to try.

Type 1very common2 practice Q

(All, Some-not) complementary pair

How to spot it:

Conclusions 'All A are B' and 'Some A are not B'. The same two terms, and neither follows alone.

Method

  1. Check that the terms match.

  2. Test each conclusion alone.

  3. If neither follows, choose 'Either I or II'.

Why it works:

A is either wholly inside B or partly outside. No third case exists.

Try this

Statements

  • All rings are metals.
  • Some metals are heavy.

Conclusions

  • I. All rings are heavy.
  • II. Some rings are not heavy.

Options

  • (A) Only I follows
  • (B) Only II follows
  • (C) Either I or II follows
  • (D) Neither I nor II follows
Show solution

  1. Same two terms: rings and heavy. The pair is 'All' and 'Some-not'.

  2. Test each alone. The statements do not fix how rings relate to heavy. Neither follows alone.

  3. Either every ring is heavy, or some ring is not. Nothing else can happen.

Answer

(C) Either I or II follows

Type 2very common2 practice Q

(Some, No) complementary pair

How to spot it:

Conclusions 'Some A are B' and 'No A are B' on the same two terms.

Method

  1. Check the terms and the pair shape.

  2. Test each alone.

  3. If neither follows, choose either-or.

Why it works:

Two groups either share a member or they do not.

Try this

Statements

  • All keys are metals.

Conclusions

  • I. Some keys are iron.
  • II. No keys are iron.

Options

  • (A) Either I or II follows
  • (B) Neither I nor II follows
  • (C) Only I follows
  • (D) Only II follows
Show solution

  1. Same two terms: keys and iron. The pair is 'Some' and 'No'.

  2. The statement does not link keys to iron, so neither follows alone.

  3. Keys and iron either share a member or do not. One of the two is always true.

Answer

(A) Either I or II follows

Type 3common3 practice Q

Fake complementary pair

How to spot it:

The conclusions look like a pair but use different terms, or use (No, Some-not), or one follows alone.

Method

  1. Compare the terms word by word.

  2. Reject the (No, Some-not) shape.

  3. If one conclusion follows alone, answer that one.

Why it works:

Both conclusions can be false together, so the either-or argument breaks.

Try this

Statements

  • All cups are dishes.
  • Some dishes are pots.

Conclusions

  • I. No cups are pots.
  • II. Some cups are not pots.

Options

  • (A) Neither I nor II follows
  • (B) Only I follows
  • (C) Only II follows
  • (D) Both I and II follow
Show solution

  1. The pair is 'No' and 'Some-not'. That is not a complementary pair.

  2. Draw every cup inside pots. Then I fails, and II fails as well.

  3. Both can be false together, so there is no either-or. The answer is neither.

Answer

(A) Neither I nor II follows

Type 4occasional2 practice Q

Either-or with three statements

How to spot it:

Three statements, but the two conclusions only ask about one pair of terms.

Method

  1. Ignore the extra statements while you check the pair shape.

  2. Test each conclusion alone. An extra statement might prove one.

  3. If neither is proved, choose either-or.

Why it works:

The pair argument needs only the two conclusions.

Try this

Statements

  • All pens are books.
  • No books are files.
  • Some files are bags.

Conclusions

  • I. Some bags are pens.
  • II. No bags are pens.

Options

  • (A) Only II follows
  • (B) Either I or II follows
  • (C) Neither I nor II follows
  • (D) Only I follows
Show solution

  1. The conclusions use bags and pens. They form the pair 'Some' and 'No'.

  2. A bag can be a pen, and a bag can fail to be one. Neither follows alone.

  3. The other statements do not settle the bags-pens link. So the answer is either-or.

Answer

(B) Either I or II follows

Type 5common

One of the pair is provable

How to spot it:

The conclusions form a legal pair, but the statements give a chain that settles one of them.

Method

  1. Notice the legal pair.

  2. Do not stop there. Test each conclusion alone first.

  3. If one follows, answer 'Only' that one.

Why it works:

A conclusion that follows in every picture makes its opposite false in every picture.

Try this

Statements

  • All pens are books.
  • All books are files.

Conclusions

  • I. All pens are files.
  • II. Some pens are not files.

Options

  • (A) Only I follows
  • (B) Only II follows
  • (C) Both I and II follow
  • (D) Neither I nor II follows
Show solution

  1. The pair is 'All' and 'Some-not', so it looks like an either-or.

  2. Test each alone first. Chain the statements: all pens are files. I follows.

  3. Because I follows alone, the answer is 'Only I'. Never choose either-or here.

Answer

(A) Only I follows

10

Shortcuts that save time

⚡ Spot the opposite pair

Look for (All, Some-not) or (Some, No) on the same two terms. Then test each alone.

Example

I. Some shirts are red. II. No shirts are red. The statements never mention red. Answer?

Show solution

  1. Same terms, and the pair is Some and No.

  2. Neither follows alone.

  3. So one of them holds in every picture.

Answer

Either I or II follows.

11

Mistakes to avoid

Where most students lose marks on this subtopic.

Mistake 01

Choosing either-or when one conclusion follows alone.

Test each conclusion alone first. If one follows, choose 'Only I' or 'Only II'.

Mistake 02

Treating 'No' and 'Some-not' as an opposite pair.

They can both be false. Only (All, Some-not) and (Some, No) are opposites.

Mistake 03

Pairing conclusions that use different terms.

Both conclusions must use the same two terms.

Mistake 04

Treating 'All' and 'No' as a pair.

Both are false when A only partly overlaps B.

Mistake 05

Skipping the pair check because the statements are long.

Extra statements only matter in the alone test. The pair shape decides the rest.

12

Quick revision

Read this the night before the exam.

  • Either-or needs neither conclusion alone and an exact opposite pair.

  • Legal pairs: (All, Some-not) and (Some, No), on the same two terms.

  • (No, Some-not) and (All, No) can both be false. They are not pairs.

  • Test each conclusion alone first. One that follows ends the either-or idea.

  • Extra statements do not change the pair shape.

13

Practice: 12 questions

Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.

Topic test · 12 questions

Suggested time 10 min · wrong answers go to your mistake notebook automatically.

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