Syllogism — AAI ATC Reasoning Lesson

Before you start

Learning objectives and outcomes

By the end of this chapter you should be able to solve any AAI ATC syllogism question by drawing, not by guessing.

Objective 1Identify the four standard statement types — All, No, Some, Some-not — and write each as a Venn diagram.

Objective 2Draw the minimum-overlap diagram for any pair of statements without redrawing three times.

Objective 3Test a conclusion by asking whether it is true in every possible diagram, not just the obvious one.

Objective 4Apply the either–or rule to complementary pairs, which is where most candidates lose the mark.

Outcome ASolve a two-statement, two-conclusion question in under 40 seconds.

Outcome BRecognise a "possibility" conclusion instantly and treat it with the opposite logic.

Subtopic 1

What a syllogism actually asks

A syllogism gives you two or more statements and asks which conclusions definitely follow. The instruction line in every AAI paper says the same thing: assume the statements are true even if they contradict real-world facts. So if a paper says "All pens are elephants", you accept it and draw it.

This is the trap. Candidates who answer from common sense lose the mark; candidates who answer from the diagram get it in seconds. There is no partial credit for "it sounds right".

The one rule that decides everything

A conclusion follows only if it is true in every possible diagram you can legally draw from the statements. If you can find even one legal diagram where the conclusion fails, the conclusion does not follow.

Follows ⇔ true in all cases · Does not follow ⇔ false in at least one case

Figure 8.1 — Statements → diagram → conclusion The three-step flow: read statement, draw circles, test each conclusion against the drawing. Upload image here

✈ AAI ATC relevance — 2 to 3 marks appear in the General Intelligence section of almost every shift

Memory trick — "Draw, don't think"

The moment you read a syllogism, your pen should already be moving. Thinking about whether crows can be sparrows is how you lose 40 seconds and still get it wrong.

EasyATC Pattern

Statements: All fans are lights. All lights are bulbs. Conclusion: All fans are bulbs. Does it follow?

Fans sit inside lights, and lights sit inside bulbs. Anything inside the innermost circle is inside the outermost one, so all fans are bulbs. A chain of two "All" statements always transfers.

ModerateATC Pattern

Statements: All doctors are humans. Some humans are tall. Conclusion: Some doctors are tall. Does it follow?

Draw the tall region overlapping humans but completely outside the doctors circle — that is a legal diagram, and in it no doctor is tall. One failing case is enough. All + Some never gives a definite Some.

HardATC Pattern

Statements: No pilot is a clerk. All clerks are graduates. Conclusion: Some graduates are not pilots. Does it follow?

Clerks exist inside graduates, and no clerk is a pilot. So that portion of the graduate circle is definitely non-pilot. Hence some graduates are certainly not pilots. This holds in every diagram, so it follows.

Subtopic 2

The four statement types

Every syllogism statement in every exam reduces to one of four forms. Learn the diagram for each and you have learned the whole chapter.

Form	Example	Diagram	What it guarantees
All A are B	All pins are bins	A circle drawn wholly inside B	Every A is a B. Nothing about extra B's.
No A is B	No pilot is a clerk	Two circles that never touch	Zero overlap, guaranteed both ways.
Some A are B	Some crows are parrots	Two circles crossing	At least one item is in both. Also gives you Some B are A.
Some A are not B	Some bins are not papers	Part of A sticking outside B	At least one A is outside B. Says nothing about B.

Figure 8.2 — The four standard Venn diagrams Four small panels side by side: All, No, Some, Some-not, each with circles labelled A and B. Upload image here

The conversion rule

Two of the four forms can be flipped safely, two cannot. This single table wins you marks on "Some ... are ..." conclusions that look too easy to be true.

All A are B → Some B are A ✔ | No A is B → No B is A ✔
Some A are B → Some B are A ✔ | Some A are not B → Some B are not A ✘

Memory trick — "ANS flips, the fourth sticks"

All, No and Some can all be reversed in some form. Only Some-not refuses to flip. If a conclusion reverses a Some-not statement, mark it "does not follow" without drawing.

Worked example — step by step

Statements: Some crows are parrots. Some parrots are sparrows. Conclusion: Some crows are sparrows.

Draw crows and parrots crossing — that satisfies statement 1.
Draw sparrows crossing parrots. Nothing forces sparrows to touch crows.
Place the sparrow circle so it overlaps only the part of parrots that lies outside crows. This is legal.
In that diagram, no crow is a sparrow. One failing case exists.
Answer: does not follow. Some + Some never gives a definite Some.

EasyATC Pattern

"Some books are pens" also definitely means:

A "Some" statement flips freely. If at least one item is in both circles, then reading the overlap from the other side is equally true. The other three options add information the statement never gave.

ModeratePYQ 2021 · Shift 2

Statements: 1. Some parrots are sparrows. 2. Some crows are parrots. Conclusions: I. Some sparrows are parrots. II. Some crows are sparrows.

Conclusion I is statement 1 read backwards, and "Some" flips safely, so it follows. Conclusion II links two Some statements through a middle term — you can always draw the sparrows away from the crows, so it fails. Only I follows.

HardPYQ 2021 · Shift 3

Statements: 1. All pins are bins. 2. All bins are not papers. Conclusions: I. Some papers are pins. II. All pins are not papers.

Statement 2 here means no bin is a paper. Pins sit entirely inside bins, so no pin can be a paper — conclusion II follows. Conclusion I claims an overlap between papers and pins, which the diagram forbids completely. Only II follows.

Subtopic 3

The Venn method — minimum overlap first

The mistake almost every beginner makes is drawing the friendliest diagram, the one where everything overlaps nicely. Then every conclusion looks true. The correct habit is the opposite: draw the least overlap the statements allow, and only add contact where a statement forces it.

Four-step routine

Underline the middle term — the word appearing in both statements.
Draw the definite statement (All / No) first. Definite shapes anchor the diagram.
Attach the indefinite statement (Some / Some-not) in the position of least contact.
Read each conclusion off the drawing. If it is not visibly forced, it does not follow.

Figure 8.3 — Minimum overlap vs friendly overlap Two diagrams of the same statement pair: the left one drawn with least contact, the right one drawn generously, with the conclusion true only in the right one. Upload image here

Memory trick — "Definite first, doubtful last"

All and No are definite; Some and Some-not are doubtful. Draw the definite one first every single time and the diagram almost builds itself.

EasyATC Pattern

In a two-statement question, which statement should be drawn first?

Definite statements fix the positions of two circles exactly, leaving only the third circle to be placed. Starting with a Some statement leaves everything floating and invites errors.

ModerateATC Pattern

Statements: All radars are screens. No screen is a runway. Conclusion: No radar is a runway. Does it follow?

All radars lie inside the screen circle, and the screen circle shares no area with runways. So no radar can touch runways in any legal diagram. All + No gives a definite No.

HardATC Pattern

Statements: Some controllers are engineers. All engineers are graduates. Conclusion: Some graduates are controllers. Does it follow?

At least one person is both a controller and an engineer. Every engineer is a graduate, so that person is also a graduate. That single person makes "some graduates are controllers" true in every diagram. Some + All in this direction does transfer.

Subtopic 4

Possibility conclusions — the logic flips

Some AAI questions phrase the conclusion as "Some A being B is a possibility". This is not the same question, and the rule inverts. A normal conclusion needs to be true in every diagram. A possibility conclusion only needs to be true in one legal diagram.

The inversion

Normal conclusion → follows if true in all cases
Possibility conclusion → follows if true in at least one case

So a possibility fails only when the statements make it impossible. If a "No" statement blocks the overlap completely, the possibility is dead; otherwise it is almost always alive.

Figure 8.4 — When a possibility dies Left panel: two circles held apart by a "No" statement, marked impossible. Right panel: circles free to move, marked possible. Upload image here

Memory trick — "Possible until proven impossible"

Treat every possibility conclusion as TRUE by default. Then hunt for a "No" statement that forbids it. No blocker, no problem — the possibility follows.

EasyATC Pattern

Statements: Some files are red. Some red things are heavy. Conclusion: All files being heavy is a possibility. Does it follow?

No statement separates files from heavy things, so you can enlarge the heavy circle to swallow the whole file circle while keeping both statements true. One legal diagram is enough for a possibility.

ModerateATC Pattern

Statements: No aircraft is a bus. All buses are vehicles. Conclusion: Some vehicles being aircraft is a possibility. Does it follow?

The "No" statement only separates aircraft from buses, not from vehicles. The vehicle circle is bigger than the bus circle, so its outer region is free to overlap aircraft. The possibility survives.

HardATC Pattern

Statements: All towers are tall. No tall thing is short. Conclusion: Some towers being short is a possibility. Does it follow?

Towers are locked entirely inside tall, and tall is entirely cut off from short. There is no legal position where any tower touches short, so the possibility is impossible. This is the rare case where a possibility fails.

Subtopic 5

The either–or rule

Sometimes neither conclusion follows on its own, yet the answer key says "Either I or II follows". This happens under two conditions that must both hold.

Both conditions must be met

1. Individually, neither conclusion follows.
2. The two conclusions share the same subject and predicate, and form a complementary pair.

Complementary pairs are: All A are B with Some A are not B; and Some A are B with No A is B. Between them they cover every possibility, so one of them must be true.

Figure 8.5 — Complementary pairs chart A two-column chart pairing All ↔ Some-not and Some ↔ No, with a note that each pair covers all possible cases. Upload image here

Memory trick — "A–SN and S–N"

Only two pairings exist: All with Some-Not, and Some with No. If the two conclusions are not one of these two pairs, either–or is not the answer, no matter how tempting it looks.

Worked example — step by step

Statements: Some strips are charts. All charts are boards. Conclusions: I. All strips are boards. II. Some strips are not boards.

Draw strips overlapping charts, and charts wholly inside boards.
Test I: the non-chart part of strips can sit outside boards, so I fails on its own.
Test II: that part can also be pulled inside boards, so II fails on its own too.
Check the pair: same subject (strips), same predicate (boards), and the forms are All and Some-not — a complementary pair.
Answer: Either I or II follows.

EasyATC Pattern

Which of these is a valid complementary pair?

Some A are B and No A is B are exact opposites — either at least one overlap exists or none does, with no third option. The other pairs leave gaps or change the subject and predicate.

ModerateATC Pattern

Statements: Some signals are lights. Conclusions: I. All signals are lights. II. Some signals are not lights. The answer is:

Neither is forced individually — the overlap may cover all signals or only part of them. But All and Some-not on the same subject and predicate form a complementary pair, so one of them is certainly true. The answer is either–or.

HardATC Pattern

Statements: All pilots are trained. Some trained people are calm. Conclusions: I. Some pilots are calm. II. No pilot is calm. The answer is:

Individually both fail — the calm region can be placed inside or outside the pilot circle. The two conclusions share subject and predicate and are the Some / No pair, which is complementary. So either I or II follows.

Exam strategy

Six tips that hold in the AAI ATC hall

Never skip the diagramEven for a two-line question. Mental syllogism is where the marks die.

Read the conclusion type firstSpot the word "possibility" before you start drawing. It changes the whole test.

Some-not is a trap word"All bins are not papers" in AAI papers means no bin is a paper. Read carefully.

Check either–or lastOnly after both conclusions have individually failed. Never before.

40 seconds, then moveIf a three-statement question resists two diagrams, mark it and come back.

Ignore real-world truthThe instruction line says so explicitly. Common sense is the enemy here.

Quick revision

Chapter summary sheet

Core ruleA conclusion follows only if true in every legal diagram.

Four formsAll, No, Some, Some-not — each has one fixed diagram.

ConversionAll → Some (reversed) ✔ · No → No ✔ · Some → Some ✔ · Some-not → ✘

All + AllGives a definite All. The chain transfers.

All + NoGives a definite No.

Some + SomeGives nothing definite. Ever.

Some + AllGives a definite Some, but only in the forward direction.

PossibilityTrue in one case is enough. Fails only when a No statement blocks it.

Either–or pairsAll ↔ Some-not, and Some ↔ No. Nothing else qualifies.

↓ Free download — Syllogism question PDF

Four pages of practice covering every question type in this chapter, with blank space left for you to draw the Venn diagrams by hand. Print it, solve it, keep it.

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End of chapter

Comprehensive assessment

Nine question formats, in the order they build difficulty. Full solutions are in the downloadable PDF above.

A · Multiple choice questions

1. Statements: All strips are boards. No board is plastic. Conclusion: No strip is plastic. Does it follow?

2. Statements: Some radars are new. All new things are costly. Which definitely follows?

3. Which pair of conclusions can produce an "either–or" answer?

4. "Some A are not B" definitely implies which of the following?

5. Statements: All charts are maps. Some maps are old. Conclusion: Some charts are old. Does it follow?

B · Assertion and reason

6. Assertion: "Some pens are books" also means "Some books are pens". Reason: A Some statement can be converted freely.

7. Assertion: A possibility conclusion follows if it is true in at least one diagram. Reason: Possibility asks what can happen, not what must happen.

C · Match the following

Column I — statement pair	Column II — definite result
(a) All A are B + All B are C	(i) No definite conclusion
(b) All A are B + No B is C	(ii) All A are C
(c) Some A are B + Some B are C	(iii) Some C are A
(d) Some A are B + All B are C	(iv) No A is C

D · Fill in the blanks

8. A conclusion follows only if it is true in possible diagrams.

9. The only statement form that cannot be converted is .

10. "All A are B" combined with "No B is C" gives the definite conclusion .

11. The two complementary pairs are All ↔ and Some ↔ .

E · True or false

12. Two "Some" statements can produce a definite conclusion.

13. "No A is B" can be reversed to "No B is A".

14. A possibility conclusion fails only when the statements make it impossible.

15. Either–or can be chosen even when one conclusion already follows on its own.

F · Short answer

16. State the minimum-overlap principle in one sentence and explain why it matters.

17. Write both complementary pairs and give one example of each.

18. Why does "Some A are not B" fail to convert? Give a counter-example.

G · Long answer

19. Explain the complete four-step Venn routine and apply it to: All controllers are staff. Some staff are trainees. Test both "Some controllers are trainees" and "Some trainees are staff".

20. Compare a normal conclusion with a possibility conclusion. Give one worked example of each where the answers differ.

H · HOTS — higher order thinking

21. Three statements: All A are B. Some B are C. No C is D. Determine every definite conclusion that can be drawn about A and D, and justify each with a diagram.

22. Construct a statement pair for which "Either I or II follows" is the answer, and prove that neither conclusion holds individually.

I · Previous year exam style

23. Statements: 1. Some parrots are sparrows. 2. Some crows are parrots. Conclusions: I. Some sparrows are parrots. II. Some crows are sparrows. PYQ 2021 · Shift 2

24. Statements: 1. All pins are bins. 2. All bins are not papers. Conclusions: I. Some papers are pins. II. All pins are not papers. PYQ 2021 · Shift 3

25. Statements: All flights are delayed. No delayed thing is cheap. Conclusions: I. No flight is cheap. II. Some delayed things are flights. ATC Pattern

J · Mixed revision test

26–35. Ten mixed questions covering all five subtopics, timed at seven minutes total. Full set with answer key is in the free PDF.

Learning objectives and outcomes

What a syllogism actually asks

The one rule that decides everything

The four statement types

The conversion rule

The Venn method — minimum overlap first

Four-step routine

Possibility conclusions — the logic flips

The inversion

The either–or rule

Both conditions must be met

Six tips that hold in the AAI ATC hall

Chapter summary sheet

↓ Free download — Syllogism question PDF

Comprehensive assessment

A · Multiple choice questions

B · Assertion and reason

C · Match the following

D · Fill in the blanks

E · True or false

F · Short answer

G · Long answer

H · HOTS — higher order thinking

I · Previous year exam style

J · Mixed revision test

Syllogism is easy. The other fourteen reasoning topics decide your rank.