Statements: All Trees are Roots. Some Roots are Branches.Conclusions:I. All Trees are Branches.II. Some Branches are Trees.

Answer: Neither I nor II follows. Thinking Process: Root is the common term. Statement 1 is 'All' (Tree=100, Root=50). Statement 2 is 'Some' (Root=50, Branch=50). Since 'Root' is 50 in both, there is NO definite relation between Trees and Branches.Exam Attack: No 100 on common term = No connection. Both conclusions cross. Neither follows.

Statements: No Car is a Bus. Some Buses are Trains.Conclusions:I. Some Trains are not Cars.II. No Train is a Car.

Answer: Only Conclusion I follows. Thinking Process: Combine Stmt 1 & 2. Node 'Bus' connects them (Bus=100 in Stmt 1). Result must be Negative. Trains (50) and Cars (100) -> 'Some Trains are not Cars' (I is True). 'No Train is a Car' makes Train 100, which is invalid since it was 50.Exam Attack: Some + No = Some Not. Conclusion I is exactly that. II is overkill.

Statements: All Lights are Fans. All Fans are Bulbs.Conclusions:I. All Lights are Bulbs.II. Some Bulbs are Lights.

Answer: Both I and II follow. Thinking Process: All A are B, All B are C -> All A are C is True. Also, Some C are A is True (reverse reading of All). Both follow perfectly.Exam Attack: Direct positive chain. A->B->C means A is fully inside C. Both conclusions naturally follow.

Statements: Some Pens are Pencils. Some Pencils are Erasers.Conclusions:I. Some Pens are Erasers.II. No Pen is an Eraser.

Answer: Either I or II follows. Thinking Process: Both statements are 'Some' (I-type). Common term 'Pencil' is 50 in both. No definite relation between Pen and Eraser. Both conclusions are individually false. Exam Attack: Check Either/Or! Subjects are same (Pen, Eraser). One is '+ve' (Some), one is '-ve' (No). They form a complementary pair. Answer is Either I or II.

Statements: All Cats are Dogs. No Dog is a Rat.Conclusions:I. No Cat is a Rat.II. Some Dogs are Cats.

Answer: Both I and II follow. Thinking Process: Cat connects to Rat via Dog (100 in Stmt 2). Result is Negative 'No Cat is Rat'. Conclusion I is True. Statement 1 converting 'All Cats are Dogs' backward gives 'Some Dogs are Cats'. Conclusion II is True.Exam Attack: Visualise target. Cats fully inside Dogs, Dogs fully separated from Rats. So Cats fully separated from Rats.

Statements: Some Apples are Oranges. All Oranges are Bananas.Conclusions:I. Some Apples are Bananas.II. All Bananas are Apples.

Answer: Only Conclusion I follows. Thinking Process: Common term is Oranges (100 in Stmt 2). Result is +ve. 'Some Apples are Bananas' -> True. Conclusion II expands Banana to 100, which is invalid.Exam Attack: 50-50 check. Bananas is 50 in Stmt 2. It can't be 100 in Conclusion II. Cross it out immediately.

Statements: No Water is Air. No Air is Fire.Conclusions:I. Some Water is Fire.II. No Water is Fire.

Answer: Either I or II follows. Thinking Process: Negative + Negative = No Definite Conclusion. Both are individually doubtful. However, Subject/Predicates match and it's a (Some + No) pair. Thus, Either/Or applies.Exam Attack: Rule: Two negative statements yield NO relation. Instantly check for Either/Or.

Statements: All Lions are Tigers. Some Tigers are Leopards.Conclusions:I. All Lions are Leopards.II. Some Leopards are Lions.

Answer: Neither I nor II follows. Thinking Process: Middle term 'Tigers' is 50 in both statements. No connection can be made between Lions and Leopards. Both conclusions are false.Exam Attack: Quick scan: Middle term not 100 anywhere. Kill all conclusions mixing the outer terms.

Statements: Some Books are Novels. No Novel is a Poem.Conclusions:I. Some Books are not Poems.II. All Books are Poems.

Answer: Only Conclusion I follows. Thinking Process: Connect Books -> Novels -> Poem. Novel is 100 in Stmt 2. Positive + Negative = Negative. 'Some Books are not Poems' is true. Conclusion II is positive, which is impossible.Exam Attack: + and - means answer MUST be -. Conclusion II is +, eliminate! Conclusion I perfectly aligns.

Statements: All Phones are Laptops. All Laptops are Tablets.Conclusions:I. Some Tablets are Phones.II. Some Tablets are Laptops.

Answer: Both I and II follow. Thinking Process: Complete chain Phone -> Laptop -> Tablet. Both conclusions are 'Some' moving backward in the chain. Backward 'Some' is always true in a Universal chain.Exam Attack: Moving outside-in on Venn diagram always gives 'Some' relations as True. Both correct!

Statements: Some Kings are Queens. All Queens are Princes. No Prince is a Knight.Conclusions:I. Some Kings are not Knights.II. All Queens are Knights.

Answer: Only Conclusion I follows. Thinking Process: Connect Kings -> Queens -> Princes -> Knights. King to Prince: Some Kings are Princes. Prince to Knight: No Prince is Knight. Combine them: Some Kings are not Knights. I follows. II is mathematically impossible as Queens are inside Princes, and no Prince is a Knight.Exam Attack: Trace the negative block! Knights cannot touch Princes. Queens are strictly inside Princes. So Knights can NEVER touch Queens. II is false immediately.

Statements: All Fruits are Veggies. Some Veggies are Sweets. No Sweet is Spicy.Conclusions:I. Some Fruits being Sweets is a possibility.II. Some Veggies are not Spicy.

Answer: Both I and II follow. Thinking Process: I: Fruits and Sweets have NO definite relation (common term Veggies is 50-50). So ANY possibility between them is TRUE. II: Veggies intersect with Sweets. Sweets can't be Spicy. The part of Veggies that are Sweets can NEVER be Spicy. So, Some Veggies are not Spicy -> True.Exam Attack: 'Possibility' of unconnected circles is ALWAYS true. Overlapping a Negative circle generates a 'Some Not'. Boom, both true.

Statements: Some Mugs are Cups. No Cup is a Glass. All Glasses are Jugs.Conclusions:I. Some Jugs are not Cups.II. Some Mugs are not Glasses.

Answer: Both I and II follow. Thinking Process: I: Glasses are inside Jugs. Glasses cannot touch Cups. So the part of Jugs that are Glasses cannot touch Cups -> Some Jugs are not Cups (True). II: Part of Mugs that are Cups cannot touch Glasses -> Some Mugs are not Glasses (True).Exam Attack: Very classic banking pattern. Overlap + Negative = 'Some Not' holds true from both sides of the negative chain.

Statements: All Stars are Planets. All Planets are Galaxies. No Galaxy is a Universe.Conclusions:I. All Stars being Universe is a possibility.II. No Planet is a Universe.

Answer: Only Conclusion II follows. Thinking Process: Galaxies cannot touch Universe. Stars and Planets are entirely inside Galaxies. So neither of them can ever touch Universe. Conclusion I is an impossible possibility (False). Conclusion II is absolutely True.Exam Attack: If the parent circle (Galaxy) is restricted, all child circles (Stars, Planets) inherit the restriction. Possibility of breaking restriction = False.

Statements: Some Boys are Men. Some Men are Old. Some Old are Wise.Conclusions:I. Some Boys are Wise.II. No Boy is Wise.

Answer: Either I or II follows. Thinking Process: A chain of 'Some' statements. Common terms never reach 100. Thus, NO relation can be established between endpoints (Boys and Wise). I and II are false. However, it's a perfect 'Some + No' Either/Or pair with identical subjects.Exam Attack: Chain of 'I' type statements -> ALL conclusions between unconnected terms are doubtful. Check for Either/Or instantly.

Statements: All Reds are Blues. No Blue is a Green. All Greens are Yellows.Conclusions:I. Some Yellows are not Blues.II. No Red is a Green.

Answer: Both I and II follow. Thinking Process: I: Greens are Yellows, Greens can't be Blues. So the Greens inside Yellows can't be Blues -> Some Yellows are not Blues. True. II: Reds are inside Blues. Blues can't be Greens -> Reds can't be Greens either. True.Exam Attack: Parent restriction hits the child (Reds can't be Green). Child restriction transfers partially to Parent (Some Yellows are not Blue). Solid concept check.

Statements: Some Papers are Woods. All Woods are Trees. No Tree is a Plant.Conclusions:I. Some Papers are not Plants.II. No Wood is a Plant.

Answer: Both I and II follow. Thinking Process: Papers overlap Woods. Woods are fully Trees. Trees can't be Plants. So Woods can't be Plants (II is True). The part of Papers that overlaps Woods cannot be Plants (I is True).Exam Attack: Everything flowing beautifully from the negative anchor 'Tree'. This is a direct deduction loop.

Statements: All Rings are Necklaces. Some Necklaces are Bracelets. No Bracelet is a Bangle.Conclusions:I. Some Rings being Bracelets is a possibility.II. Some Necklaces are not Bangles.

Answer: Both I and II follow. Thinking Process: Rings and Bracelets have no definite link. So possibility is True. Necklaces overlap Bracelets, which can't be Bangles. So some Necklaces are not Bangles. True.Exam Attack: Unknown relation = Possibility True. Overlap with a negative = Some Not True.

Statements: No Book is a Copy. Some Copies are Pages. All Pages are Covers.Conclusions:I. Some Pages are not Books.II. Some Covers are not Books.

Answer: Both I and II follow. Thinking Process: Copies can't be Books. Pages overlap Copies -> Some Pages are not Books. Covers contain Pages, which overlap Copies -> Some Covers are not Books. Both follow structurally.Exam Attack: Trace the restriction 'No Book is Copy' upwards through the 'All/Some' chain.

Statements: Some Apples are Bananas. Some Bananas are Cherries. Some Cherries are Dates.Conclusions:I. All Apples being Dates is a possibility.II. All Dates being Bananas is a possibility.

Answer: Both I and II follow. Thinking Process: Since all are 'Some' statements, and there are NO negative statements, ALL positive possibilities between unconnected elements are infinitely TRUE.Exam Attack: In an all-positive 'Some' chain, ANY possibility is True. Zero hesitation required!

Statements: Only a few Rivers are Oceans. All Oceans are Seas. No Sea is a Lake.Conclusions:I. All Rivers being Oceans is a possibility.II. All Rivers being Seas is a possibility.

Answer: Only Conclusion II follows. Thinking Process: 'Only a few Rivers are Oceans' means Some Rivers are Oceans AND Some Rivers are NOT Oceans. So, ALL Rivers can NEVER be Oceans (I is False). However, 'Some Rivers are not Oceans' does NOT restrict Rivers from being inside 'Seas'. So ALL Rivers can be Seas (II is True).Exam Attack: 'Only A few A are B' instantly kills 'All A can be B'. But the parent circle 'Seas' is huge, A can easily jump inside Seas while avoiding making contact with all of B.

Statements: Only Books are Novels. Some Books are Magazines. No Magazine is a Journal.Conclusions:I. Some Novels being Magazines is a possibility.II. No Novel is a Journal.

Answer: Only Conclusion II follows. Thinking Process: 'Only A is B' means 'All B is A' AND B has a restriction to NEVER touch anything else. So, Novels = restricted entity. Novel can NEVER touch Magazines (Possibility I is False). Novel will NEVER touch Journal (II is absolutely Definite and True).Exam Attack: 'Only' creates a toxic element (Novel). Novel rejects ANY connection except Book. Therefore, 'No Novel is X' will ALWAYS be True.

Statements: Only a few Mouses are Keyboards. Only a few Keyboards are Monitors. All Monitors are Printers.Conclusions:I. Some Mouses can never be Monitors.II. All Keyboards being Printers is a possibility.

Answer: Only Conclusion II follows. Thinking Process: I: Mouses and Monitors have no direct negative relation. So Mouses CAN be Monitors. 'Can never be' is False. II: 'Only a few K are M' means All K cannot be M. But K CAN be inside the larger circle Printers without touching all of M. So II is True.Exam Attack: 'Can never be' = Definite Some Not. Can we prove 'Some Mouse are not Monitors'? No. So False. For II, parent circle absorbs anything!

Statements: Only a few Reds are Greens. All Greens are Yellows. Only a few Yellows are Blacks.Conclusions:I. All Reds being Black is a possibility.II. Some Yellows are not Greens.

Answer: Only Conclusion I follows. Thinking Process: I: Reds and Blacks are at opposite ends of the chain with no definite negative block hitting ALL Reds. So possibility is True. II: 'All Greens are Yellows' does not mathematically guarantee 'Some Yellows are not Greens'. It's Doubtful, hence False.Exam Attack: Moving outside-in (Yellow to Green) 'All' is doubtful, 'Some' is true. 'Some Not' is strictly unproven without a negative statement. Only I rocks.

Statements: Only Doctors are Nurses. Some Doctors are Patients. Only a few Patients are Cured.Conclusions:I. Some Nurses being Patients is a possibility.II. All Patients being Cured is a possibility.

Answer: Neither I nor II follows. Thinking Process: I: Nurse is restricted by 'Only'. It cannot interact with Patients. Possibility False. II: 'Only a few P are C' explicitly means 'Some P are NOT C'. So ALL Patients can NEVER be Cured. False.Exam Attack: Two fatal traps in one question. The restriction of 'Only' kills I. The inherent negative of 'Only a few' kills II. Neither follows.

Statements: No City is a Village. Only a few Villages are Towns. All Towns are Districts.Conclusions:I. All Villages being Districts is a possibility.II. Some Districts are not Cities.

Answer: Both I and II follow. Thinking Process: I: 'Only a few V are T' prevents V from being fully inside T. But D is a bigger circle. V can be fully inside D. True. II: Towns overlap Villages. Villages can't be Cities. Districts completely enclose Towns. So the part of Districts that is Villages cannot be Cities -> True.Exam Attack: Beautiful logic test. The restriction is bound to T, not D. And the negative anchor works its magic backward.

Reverse Syllogism - Observe the Conclusions and find the correct Statements.Conclusions:I. Some Bottles are not Caps.II. All Caps being Jars is a possibility.

Answer: Only Statement I. Thinking Process: For I to be true, we need a negative statement linking Bottle and Cap. Let's check Option A: Some Bottles are Mugs. No Mug is a Cap. This generates 'Some Bottles are not Caps'. Perfect. Let's check II in Option A: No Mug is Cap. All Mugs are Jars. Caps and Jars have no strong rejection, so possibility is true.Exam Attack: Always look for the Negative conclusion first. 'Some Bottle are not Caps' demands a No/Some-not link involving Bottles.

Reverse SyllogismConclusions:I. No Square is a Triangle.II. Some Circles are Rectangles.

Answer: Only Statement II. Thinking Process: To prove 'No Square is Triangle', we need an E-type statement blocking them entirely. Look at Option B: 'No Square is Polygon. All Triangles are Polygons.' This perfectly means No Square is a Triangle. Check II: 'All Rectangles are Circles.' which means 'Some Circles are Rectangles'. This fits perfectly.Exam Attack: The 'No' deduction is easiest. Find the anchor (Polygon) that separates the two entities completely!

Look at Conclusions, find Statements.Conclusions:I. All A being D is a possibility.II. Some B are not C.

Answer: Only Statement III. Thinking Process: To get 'Some B are not C', we need an 'Only a few B are C' or a negative path like 'B is X, no X is C'. Look at Option D: 'Only a few B are X. No X is C.' This gives Some B are not C. For possibility: 'All A are B', A is inside B. It can expand into D.Exam Attack: Scan options for 'No' or 'Only a few' relating to B and C.

Conclusions:I. Some Water is definitely not Ice.II. Only a few Clouds are Water.

Answer: Either I or II follows. Thinking Process: Conclusion II is highly specific. It means 'Some Clouds are Water' AND 'Some Clouds are not Water'. The statements MUST have exactly 'Only a few Clouds are Water' to trigger this unconditionally, or a combination. Option C: 'Only a few Clouds are Water. All Water is Liquid. No Liquid is Ice.' This perfectly satisfies both! (Water -> Liquid -> No Ice means No Water is Ice, so Some Water is definitely not Ice is True).Exam Attack: If a conclusion has 'Only a few', look for it directly in the statements. It rarely derives from anything else successfully.

Home/Rajasthan 4th Grade Exam/Reasoning Ability/

Syllogism (Mains & Prelims Level)

Master this topic with zero to advance depth.

Expert Answer & Key Takeaways

Mastering Syllogism (Mains & Prelims Level) is essential for high-fidelity technical architecture and senior engineering roles in 2026.

1. Core Concepts & Propositions

Syllogism deductions rely on 4 standard propositions:
• A (All): Universal Positive (e.g., All A are B).
• E (No): Universal Negative (e.g., No A is B).
• I (Some): Particular Positive (e.g., Some A are B).
• O (Some...Not): Particular Negative (e.g., Some A are not B).

2. Venn Diagram Method & Conversions

When using Venn Diagrams, always draw the Minimum Overlapping Diagram. A conclusion is 'Definite' only if it holds true in ALL possible diagrams.
Standard Conversions:
• All A are B converts to Some B are A.
• No A is B converts to No B is A and Some B are not A.
• Some A are B converts to Some B are A.
• Some A are not B CANNOT be strictly converted.

3. The '100-50' Tick-Cross Method (Exam Attack)

For speed, assign values to Subject and Predicate:
• A (All): Sub=100, Pred=50 (+)
• E (No): Sub=100, Pred=100 (-)
• I (Some): Sub=50, Pred=50 (+)
• O (Some..Not): Sub=50, Pred=100 (-)

Rules:
1. Positive statements give Positive conclusions. Negative gives Negative.
2. If linking two statements, the common term MUST have at least one 100.
3. Value Check: A value of 50 in the statement cannot become 100 in the conclusion (You can't spend 100 if you only earn 50).

4. 'Only' & 'Only a Few' (Mains Specific)

• Only A is B: Means 'All B is A' AND B cannot overlap with anything else. Think of B as a restricted entity.
• Only a few A are B: This means 'Some A are B' AND 'Some A are NOT B'. It is a combination statement. Conclusion 'All A are B is a possibility' is strictly FALSE. But 'All B are A is a possibility' is TRUE.

5. Either/Or & Possibility Rules

Either/Or Conditions:
1. Both conclusions must be individually false (doubtful).
2. Subjects and Predicates must be exactly the same.
3. They must form a complementary pair: (Some + No) or (All + Some...Not) or (Some + Some...Not).

Possibility: If the relation between two elements is 'unknown' or 'doubtful', ANY possibility between them is TRUE.

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Syllogism (Mains & Prelims Level)

Expert Answer & Key Takeaways

1. Core Concepts & Propositions

2. Venn Diagram Method & Conversions

3. The '100-50' Tick-Cross Method (Exam Attack)

4. 'Only' & 'Only a Few' (Mains Specific)

5. Either/Or & Possibility Rules

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