Logical Reasoning · Lesson 04

Master Syllogism
with circles, not pages.

Syllogism is a small ruleset of statements like "All A are B" — and the conclusions that must follow. Draw two circles, and the question solves itself.

Learning time

22 min · self-paced

Exam weight

3–5 questions / set

Sections

10 modules

Start learning Skim the cheat sheet

Some A are B · Some B are A

Topic map

9 sections, in the order they actually build on each other.

A 1:1 path from "what is a syllogism statement" to "I can solve any 3-statement question in under 90 seconds."

Topic 01

Statement meaning

Read every word: "all", "some", "no" change everything.

Topic 02

Venn representation

Convert any statement into 1–2 circles you can see.

Topic 03

Direct conclusions

What must follow vs. what only could be true.

Topic 04

Reverse traps

All A are B ≠ All B are A. The most missed rule.

Topic 05

Possibility logic

The "Some A can be B" pattern in possibility cases.

Topic 06

Negative statements

How "No" flows — and where it secretly breaks.

Topic 07

Either-or logic

When both conclusions are individually unsure but one must be true.

Topic 08

Common tricks

High-frequency examiner setups and how they fool you.

Topic 09

Mastery check

Mini test + revision summary to lock it in.

Foundation · 01

There are only four statement types. Memorise these.

Every syllogism question is built from these four atoms. Tap any one to see what it really claims, what it guarantees, and where it traps people.

Interactive4 atoms

"All A are B"

Every member of A is also a member of B.

✓ Guaranteed

Pick any A — it lives inside B. There are no A’s outside B.

✗ Don't assume

It does NOT say all B are A. B can contain other things too — drink an apple is a fruit, but a fruit need not be an apple.

Logic code

Type A · Universal Affirmative

Try it yourself

Set the premises and let the circles force the conclusion.

Change the two statements, watch the Venn diagrams update, and see whether the chain really forces a conclusion from A to C.

Premise 1 - "__ A are B"

Premise 2 - "__ B are C"

Valid: All A are C A sits fully inside B, and B sits fully inside C, so the full chain is forced.

When the statement is definite, the diagrams act like proof. If multiple valid diagrams exist, the conclusion does not follow.

All A are B

All B are C

Method · 02

The 4-step method that solves every syllogism, every time.

Internalise this loop. The fastest solvers do this in under 60 seconds, automatically.

STEP 1

Read each statement

Underline the quantifier first — All, Some, No, Some-not. That word decides everything.

STEP 2

Convert to circles

Draw each statement as 2 circles. One per noun. The relation between them is your statement type.

STEP 3

Combine relations

Overlay all the circles into one picture. The shared terms link the statements together.

STEP 4

Test each conclusion

For each conclusion, ask: is it forced by my picture? If you can imagine a counter-picture, it doesn’t follow.

Pro tip. The most common reason people get syllogism wrong is they skip step 2 and try to reason in English. Always draw the circles. Always.

Question types · 03

The 6 formats every exam recycles.

Once you can name the format in the first 5 seconds, your brain knows exactly which mental subroutine to run. That's most of speed.

Two statements + two conclusions

Type 01 · ~45 sec target

What it looks like

Two given statements, two numbered conclusions (I and II). You must mark which conclusion(s) follow.

How to identify

Smallest, cleanest format. Default in SBI PO, IBPS Clerk Pre, RBI Assistant.

How to solve

Draw both statements as one combined diagram, then check each conclusion against it independently.

Mini example. Statements: All cats are dogs. All dogs are pets. → Conclusion I: All cats are pets. Conclusion II: Some pets are cats.

Trap: Conclusion II is "Some pets are cats" — which IS valid here because of conversion. Most students miss it.

Three statements + multiple conclusions

Type 02 · ~90 sec target

What it looks like

Three statements (more linked terms), three or four conclusions. Mains-level intensity.

How to identify

You'll see three different nouns chaining together — A↔B, B↔C, C↔D. Common in IBPS PO Mains, SBI PO Mains.

How to solve

Chain them — match nouns to pair the statements, then resolve in order. Track which terms are linked, which are isolated.

Mini example. Some pens are books. All books are bags. No bag is a chair. → Test multiple conclusions about pens, chairs and bags.

Trap: Skipping a statement because it "looks irrelevant". Every statement contributes — at minimum, it rules out a possibility.

Possibility-based conclusions

Type 03 · ~75 sec target

What it looks like

Conclusions phrased with "can be", "is a possibility", or "possibly".

How to identify

Watch for the keyword "possibility" or "can be". Standard issue in PO Mains-level reasoning.

How to solve

A possibility conclusion follows if you can draw at least one valid diagram where it is true — without breaking the given statements.

Mini example. Statements: Some teachers are women. No woman is a player. → Conclusion: All teachers being players is a possibility.

Trap: Students reject possibility conclusions because the "default" diagram doesn't show it. Possibility ≠ certainty — try drawing it.

Either-or conclusions

Type 04 · ~60 sec target

What it looks like

Two conclusions about the same pair of nouns — one positive, one negative.

How to identify

Like "Some A are B" AND "No A is B" together as two conclusions. They're opposites of each other.

How to solve

If neither conclusion individually follows — but their combination covers all possibilities — answer: Either I or II follows.

Mini example. Conclusion I: Some books are pens. Conclusion II: No book is a pen. → Either I or II follows.

Trap: Marking "Either-or" without checking the complementary pair test. The two must exhaust all cases.

Negative-only conclusions

Type 05 · ~50 sec target

What it looks like

All conclusions framed as "No X is Y" or "Some X are not Y".

How to identify

Heavy use of "no" and "not". You'll need to track which circles are completely separate.

How to solve

A negative conclusion holds only if every possible diagram keeps the two circles apart (or non-overlapping in the relevant zone).

Mini example. All hats are caps. No cap is a shoe. → Conclusion: No hat is a shoe. (Follows)

Trap: Inferring "Some are not" without ruling out the "all" case. If "all hats are shoes" is still drawable, "some hats are not shoes" doesn't follow.

Statement chains with reversed nouns

Type 06 · ~80 sec target

What it looks like

Statements stay structurally similar but the nouns swap order — testing whether you mechanically convert.

How to identify

Look for "All B are A" right after seeing "All A are B" — the order swap is the entire trick.

How to solve

Never auto-convert "All A are B" to "All B are A". Re-draw circles from scratch when the noun order flips.

Mini example. All artists are dancers. All dancers are singers. vs. All dancers are artists. All singers are dancers.

Trap: Speed-reading and assuming both are the same chain. They produce different diagrams.

Worked examples · 04

Watch three problems solved circle by circle.

Same method, three difficulty levels. Step through manually — or replay the animation.

Statements

Statement 1All cats are dogs.

Statement 2All dogs are pets.

Conclusions

Conc IAll cats are pets.

Conc IISome pets are cats.

Conc IIIAll pets are cats.

Solve step by step

Step 1. Read carefully. Note both statements are universal — "All".

1 / 5

Common traps · 05

The 6 mistakes that cost most aspirants 2 marks per set.

Memorise these. They show up in nearly every paper, in slightly different costumes.

Trap 01 · The reverse trap

All A are B → All B are A

Universal statements don't reverse. They convert only into "Some B are A".

Trap 02 · "Some" trap

"Some A are B" means "many" or "most"

"Some" can mean 1. Or all. It only guarantees at least one overlap.

Trap 03 · Possibility ≠ certainty

If the picture shows it, it follows

A conclusion follows only if every valid picture supports it — not just yours.

Trap 04 · The "no extra info" trap

Adding what feels obvious from real life

Syllogism is pure logic. "Cats are animals" isn't given — don't use it.

Trap 05 · Either-or confusion

Marking "Either or" any time both don't follow

Only valid when the two conclusions are complementary (cover all cases) — one positive, one negative on the same pair.

Trap 06 · Negative trap

Combining two negatives into a conclusion

From two negative statements, you generally cannot conclude anything definite. Be suspicious.

Tips & tricks · 06

Six tactical moves used by 99-percentile solvers.

Not theory. Small habit-level shifts you can apply on your very next practice set.

TIP 01

Underline quantifiers first

Before drawing, circle the words All, Some, No, Not-all. It anchors your brain to the right diagram.

TIP 02

Always assume disjoint first

If a relation between two terms isn't given, start by drawing them apart. Then test if they MUST overlap.

TIP 03

For "possibility", reverse the question

Ask: can I draw any valid diagram where this is true? If yes → possibility follows.

TIP 04

Check either-or last

If neither conclusion holds individually but they're opposites on the same pair, mark "Either or".

TIP 05

Conversions are free

"All A are B" → "Some B are A" always works. "No A is B" → "No B is A" always works.

TIP 06

Skip if stuck — never camp

Syllogism rewards rhythm. Stuck past 90 seconds? Flag it and move. Come back fresh.

Mini practice · 07

Try it on 4 questions — instant feedback included.

Mixed difficulty. No timer pressure. Get an explanation for every answer.

Question 1 of 4Easy

Score · 0/4

Which conclusion necessarily follows?

S1. All birds are eagles.

S2. All eagles are sharp.

Streak target: 3 in a row.

Revision · 08

One-page cheat sheet to revisit before the exam.

Print it, screenshot it, or just glance at it in the last 5 minutes before your slot.

Statement → conversion rules

Statement	Type	Converts to	Reverses?
All A are B	Universal +	Some B are A	No
Some A are B	Particular +	Some B are A	Yes
No A is B	Universal −	No B is A	Yes
Some A are not B	Particular −	—	No

Combination quick rules

All + All	→ All (chains transitively)
All + No	→ No (negation propagates)
Some + All	→ Some (downstream)
Some + No	→ Some are not
No + No	→ nothing definite
Some + Some	→ nothing definite

Last-minute reminders

01Quantifier first, nouns second. Underline before drawing.
02"All A are B" never gives you "All B are A".
03"Some" = at least one. Not "many". Not "most".
04For possibility: just need one valid diagram.
05Negative statements are symmetric. "No A is B" ⇒ "No B is A".
06Two negatives → nothing definite. Always.
07Either-or only when conclusions are complementary.
08Don't bring outside knowledge in. It's pure logic.

What's next · 09

You've finished the lesson. Time to lock it in.

Choose one — practice the hard stuff, queue the next topic, or revisit what tripped you up earlier.

Practice 20 syllogism questions

Adaptive difficulty, instant explanations, mistakes auto-added to your notebook. ~18 minutes.

Start practice

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Up next: Seating arrangement. Builds on circular logic.

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