Syllogism for Punjab Police SI

Answer: 1 — I, II, III follow

Draw the two premises. 'Some boxes are dogs' means the Boxes circle and the Dogs circle overlap; 'All dogs are pens' means the Dogs circle lies wholly inside the Pens circle. ```puzzle:venn Boxes x Dogs Dogs in Pens ``` - I. Some boxes are pens — follows. The boxes that are dogs are inside Pens, so that overlapping part is both Boxes and Pens. - II. Some pens are boxes — follows. A particular affirmative statement can always be converted, so it is simply conclusion I read the other way round. - III. Some pens are dogs — follows. 'All dogs are pens' plus the fact that dogs exist gives the converse by limitation: at least some pens are dogs. - IV. All pens are dogs — does not follow. This would reverse a universal affirmative, which is invalid: the Pens circle may be much larger than the Dogs circle, with plenty of pens that are not dogs. So I, II and III follow and IV does not. (Checking every finite arrangement of up to four elements confirms exactly this.)

Answer: 2 — Only conclusion I follows.

Both premises are universal affirmatives, so the classes nest one inside the next: every cup lies inside the circle of eyes, and every eye lies inside the circle of tables. ```puzzle:venn Cups in Eyes Eyes in Tables ``` From the nesting, every cup is a table. Conclusion I says some tables are cups — since cups exist and all of them are tables, at least a part of 'tables' is cups, so I follows. Conclusion II says some cups are not tables, which directly contradicts what the premises force; it cannot follow. Only I, so option 2. Option 3 is the trap for a candidate who accepts both an affirmative and its own negation, and option 1 for one who refuses conclusion I on the ground that the premises never mention tables and cups in the same sentence — but the chain is exactly what a syllogism is for.

Answer: 4 — Only conclusion 2 follows

Both premises are particular affirmatives ('Some A are B'), and two particular premises can never yield a definite conclusion linking the two end terms. Conclusion 1, 'Some desks are tables', therefore does not follow: the chairs that happen to be desks need not be any of the chairs that happen to be tables, so the tables and the desks may have nothing at all in common. Conclusion 2, 'Some desks are chairs', is simply the converse of the second premise — 'Some chairs are desks' and 'Some desks are chairs' say exactly the same thing, and the conversion of a particular affirmative is always valid. So only conclusion 2 follows. ```puzzle:venn Tables x Chairs Chairs x Desks ``` Option 3 is the tempting wrong answer because the two premises share the middle term 'chairs' and look as if they chain together, but a chain needs at least one universal premise.

Answer: 1 — Only conclusions (II) and (III) follow.

Take the premises as given: all teachers are intelligent, and some students are teachers. Conclusion II, 'Some teachers are students', is simply the converse of premise B and always holds — if some students are teachers then some teachers are students. Conclusion III, 'Some students are intelligent', holds too: those students who are teachers are intelligent by premise A, so at least some students are intelligent. Conclusion I, 'All students are intelligent', does not follow — the premises say nothing whatever about the students who are not teachers, so one of them may be unintelligent without contradicting either statement. Conclusion IV, 'No student is intelligent', directly contradicts III and fails at once. The valid set is therefore exactly {II, III}.

Answer: 1 — Only conclusion (I) follows

Draw the premises: ```puzzle:venn smiles in lips lips x teeth ``` Conclusion (I) 'Some teeth are lips' is just the converse of the given 'Some lips are teeth'. A particular affirmative converts freely, so it follows. Conclusion (II) 'At least some smiles are teeth' does not follow. The smiles circle sits wholly inside lips, but nothing forces it into the part of lips that overlaps teeth — the overlap can be drawn entirely outside the smiles circle, and then no smile is a tooth. A possibility is not a definite conclusion — a “may be” conclusion is judged by whether one allowed drawing permits it, not by whether every drawing forces it.

Answer: 2 — Only conclusion I follows.

Draw the premises as sets. ```puzzle:venn Boys x Smart Smart x Cheaters Cheaters in Optimists ``` Conclusion I: the second premise guarantees at least one thing that is both smart and a cheater, and the third premise puts every cheater inside optimists. That same thing is therefore both smart and an optimist, so 'Some optimists are smart' must be true — I follows. Conclusion II: the boys overlap smart, and the cheaters also overlap smart, but nothing forces those two overlaps to meet. The smart boys could be entirely separate from the smart cheaters, so II does not follow. A pair of particular ('some') premises never yields a definite conclusion between their end terms — this is the standard trap and is exactly why option 4 is wrong. Conclusion III: it depends on II, since boys can only be shown to be optimists through the cheaters, so it fails for the same reason. Only conclusion I follows.

Answer: 4 — If neither conclusion I nor conclusion II follows

Take the conclusions one at a time. I. 'No liquid is an air.' The statements link air only to solid (No air is a solid) and link liquid only to solid (Some solids are not liquid). Air and liquid are never joined, so nothing at all follows about them — a liquid could perfectly well be an air. I does not follow. II. 'At least some liquids are iron.' The only liquid statement is a particular negative, 'Some solids are not liquid', and a particular negative never yields a positive conclusion; it tells you nothing about any liquid actually existing inside the solid class. Since iron is reached only through solid (All solids are iron), no liquid can be tied to iron. II does not follow. Option 2 is the trap, obtained by misreading 'Some solids are not liquid' as 'Some solids are liquid'. Neither follows,

Answer: 1 — Only conclusions I and IV follow.

Chain the second and third statements: some pencils are bags, and every bag is a sharpener, so those same pencils are sharpeners. That gives 'Some pencils are sharpeners' (conclusion IV), and a 'some' statement converts, so 'Some sharpeners are pencils' (conclusion I) follows as well. Both I and IV are established. Conclusions II and III both need an overlap between pens and bags. All that is known about pens is that they sit inside pencils; the pencils that are bags need not include any pen, so the pen circle can be drawn entirely inside the non-bag part of pencils. Nothing forces 'Some bags are pens' or 'Some sharpeners are pens', so III and II do not follow. ```puzzle:venn Pen in Pencil Pencil x Bag Bag in Sharpener ``` Drawn this way, the pen circle can be placed wholly in the part of pencils that lies outside bags, so every statement stays true while II and III come out false - which is exactly why they are not conclusions.

Answer: 3 — Only II follows

Treat the statements as true and ask of each conclusion: must it hold in every arrangement that satisfies them? Statements: Some pink are not yellow. All orange are pink. Some green are yellow. Conclusion I — "All oranges are green." Nothing in the statements ties orange to green. Orange sits wholly inside pink; green is linked only to yellow, and only by a "some". You can draw orange entirely inside pink with no overlap at all with green, and every statement still holds. A definite "All ... are ..." can only be drawn from a definite premise, never from a "some". So I does not follow. Conclusion II — "Some pink are not orange is a possibility." "All orange are pink" places orange inside pink, but it never says the two sets coincide. Pink is free to be the bigger circle, so pink members outside orange may exist. Since II claims only a possibility, and that possibility is consistent with all three statements, II follows. The tempting wrong answer is (B) Both follow: candidates see orange, pink, yellow and green all named and assume a chain runs through them. It does not — the only definite link is orange ⊂ pink, and the two "some" statements cannot carry a universal conclusion. Only II follows — option 3.

Answer: 4 — Neither conclusion I nor II follow.

Statements: All grapes are orange. Some grapes are fruits. Some kiwi are fruits. Conclusion I — "Some kiwi are grapes." Kiwi and grapes meet only through the word "fruits", and both links are "some". Two "some" statements sharing a middle term give no valid conclusion: the kiwi that are fruits and the grapes that are fruits can be completely different fruits. So I does not follow. Conclusion II — "Some oranges are not kiwi." All grapes are orange, but orange may be a much larger set, and nothing stops every single orange from also being a kiwi. Draw orange entirely inside kiwi: all grapes are then orange and kiwi, some grapes are still fruits, some kiwi are still fruits — every statement holds and yet no orange is outside kiwi. Since a counter-arrangement exists, II is not forced either. The trap is (B): "Some oranges are not kiwi" feels safe because orange and kiwi were never connected — but an unstated connection is a permission, not a prohibition. A negative conclusion needs a negative or universal premise, and there is none here. Neither conclusion follows — option 4.

Answer: 2 — None of the conclusions follow

Take the statements at face value and look for a chain joining the two terms in each conclusion. ```puzzle:venn pacifiers, rainbows: in rainbows, spinach: x spaghettis, trains: x ``` - Conclusion I (Some spaghettis are pacifiers): spaghetti is linked only to trains. Nothing ties spaghetti to rainbows or to pacifiers, so no link — does not follow. - Conclusion II (Some tomatoes are rainbows): tomatoes are never mentioned in any statement. A term that does not appear cannot be concluded about — does not follow. - Conclusion III (Some pacifiers are trains): pacifiers connect up to rainbows only, trains connect to spaghetti only; the two halves never meet — does not follow. Since I and III both fail independently, they cannot form an either-or pair either, so option 1 is wrong. Hence option 2: none of the conclusions follow.

Answer: 2 — All I, II and III follow

Draw the three statements: ```puzzle:venn Brown in Black Brown | White White in Blue ``` I. Browns exist, every brown is black, and no brown is white, so those browns are blacks that are not whites — some blacks are not whites. Follows. II. Whites exist and all of them are blues, while no brown is white, so those blues are not browns — some blues are not browns. Follows. III. This is a possibility conclusion. Nothing forbids a blue from being black (blacks and blues are linked only through the brown and white circles), so the overlap is possible. A "may be" conclusion follows whenever the case is not ruled out. Follows. All three follow, so option 3 (only I and II) is the tempting but incomplete choice.

Answer: 1 — All I, II and III follow

Draw the three statements: ```puzzle:venn Cup in Mug Cup | Plate Saucer in Plate ``` - I: Some mugs are not plates — every cup is a mug, and no cup is a plate, so the cups themselves are mugs that are not plates. Follows. - II: No saucer is a cup — all saucers lie inside Plate, and Cup is wholly outside Plate, so the two cannot meet. Follows. - III: Some plates may be mugs — this is a possibility statement. Nothing in the statements forbids a mug (a non-cup mug) from being a plate, so the possibility stands. Follows. The usual trap is to reject III because no definite link is proved; but a "may be" conclusion only needs the case to be not impossible. All three follow.

Answer: 1 — Conclusion II and III follow

Draw the three statements: ```puzzle:venn laptops in mice mice in desktops keyboards in desktops ``` Laptops sit inside mice, mice sit inside desktops, and keyboards sit inside desktops as a separate block. - Conclusion I — Some keyboards are mice: does not follow. Keyboards and mice are both inside desktops, but nothing forces them to overlap; the keyboard circle can be drawn entirely clear of the mice circle. - Conclusion II — Some desktops are mice: follows. "All mice are desktops" guarantees at least one mouse, and that mouse is a desktop, so the converse particular is valid. - Conclusion III — Some desktops are laptops: follows. All laptops are mice and all mice are desktops, so all laptops are desktops, and the particular converse again holds. II and III follow —

Answer: 3 — Only conclusion I follows

The third statement, 'Some orange is flower', is an I-type (particular affirmative) premise, and an I-type proposition converts simply: if some orange is flower, then some flower is orange. So Conclusion I follows directly from the given data. Conclusion II says 'All flower is apple', which flatly contradicts the first statement 'No flower is apple' — it can never follow. Conclusion III says 'No flower is orange', which contradicts Conclusion I, and Conclusion I is definitely true. So III is false. (The tempting trap is to chain 'No flower is apple' with 'No apple is orange' and conclude something about flower and orange — but two negative premises yield no valid conclusion.) Only Conclusion I follows. ```puzzle:venn flower | apple apple | orange orange x flower ```

Answer: 1 — Only conclusion I follows

```puzzle:venn Erasers in Sharpeners Sharpeners x Pencils Pencils x Pens ``` Conclusion I: "All erasers are sharpeners" converts to the particular "Some sharpeners are erasers" — a valid immediate inference, so I follows. Conclusion II: the eraser circle sits inside sharpeners, but the sharpener–pencil overlap need not touch it; the erasers can lie entirely in the non-pencil part of sharpeners. So II does not follow. Conclusion III: it flatly contradicts the given "Some pencils are pen", so it cannot follow. Only I survives. Option 2 tempts anyone who treats "some" as implying "some not" for pens.

Answer: 4 — Only conclusions I and III follow

'Most triangles are circles' is a particular affirmative: some triangles are circles. A particular affirmative converts, so 'some circles are triangles' is valid — conclusion I follows. 'No circle is a square' is a universal negative, and a universal negative converts too, so 'no square is a circle' is valid — conclusion III follows. Conclusion II reverses a given universal: the statements say all squares are triangles, which never licenses 'all triangles are squares' (the triangles that are circles cannot be squares at all). ```puzzle:venn Triangle x Circle Circle | Square Square in Triangle ```

Answer: 4 — Only conclusion III follows

Draw the three statements: ```puzzle:venn Monkeys in Sugars Sugars x Berries Sugars | Hens ``` Conclusion I fails: all monkeys lie inside sugars and no sugar is a hen, so in fact no monkey can be a hen. Conclusion II fails: the berries that overlap sugars need not be the monkey part of sugars, so the overlap is only possible, not certain. Conclusion III holds: some sugars are berries, and none of those sugars is a hen, so those berries are definitely not hens. I and III are not a complementary pair (they use different terms), so the 'either-or' of option 1 does not apply.

Answer: 3 — Only I and III follow

Conclusion I: 'No piano is drum' plus 'Some drums are tabla' gives 'Some tabla are not piano' — those tabla that are drums can never be piano, so I follows. Conclusion II: 'No guitar is piano' and 'No piano is drum' are two negative premises; from two negatives no definite conclusion can be drawn, so 'No drum is guitar' does not follow. Conclusion III is a possibility statement, and nothing in the premises forbids the tabla that are not drums from overlapping piano, so 'Some piano can be tabla' is a valid possibility and follows. I and III follow. Option 4 wrongly admits the definite negative II. Answer: option 3. ```puzzle:venn Guitar | Piano Piano | Drum Drum x Tabla ```

Answer: 2 — Statement II is the cause and statement I is its effect

A cause must be able to come before its effect and must be able to produce it. Statement II describes a standing, structural condition — small private and co-operative banks are financially too weak to stand up to the large public sector banks. Statement I describes a single recent regulatory action — the RBI has just put restrictions on a few small banks. A regulator imposes restrictions on weak banks precisely because they are weak, so the weakness (II) is the cause and the restrictions (I) are its effect. Option 1 reverses this and cannot work: restrictions on only 'a few' small banks could not make the whole class of small banks structurally uncompetitive, and II is a long-standing condition while I is described as recent. Option 3 fails because the two are clearly linked, not independent, and option 4 fails because no third common cause is available that would produce both the RBI's action and the sector's weakness.

Answer: 3 — Both the statements I and II are effects of independent causes

Ask, for each direction, whether one statement could produce the other. If rising crude prices (II) were the cause, the normal effect on the domestic market would be a rise in petrol and diesel prices, not the unchanged prices of statement I — so II cannot be the cause of I, and option 2 is out. Domestic retail prices in one country obviously cannot hold up or push down world crude prices, so option 1 is out as well. Nor is there a single common cause behind both: world crude prices are set by global demand and OPEC supply decisions, while unchanged domestic pump prices are the result of a separate domestic factor (government price control, subsidy or the absorption of the increase by oil marketing companies through taxes and margins). The two facts therefore arise from separate, independent causes, which is exactly what option 3 says.

Answer: 4 — By the performance of the condition of the proposal

The closing clause of the passage answers the question directly: where the proposer intimates that it is enough to act on the proposal without communicating acceptance to him, 'performance of the condition is a sufficient acceptance without notice'. So acceptance can be shown by performing the condition attached to the proposal. Option 3 says the opposite of what is asked, since the question is precisely about acceptance without communication, and options 1 and 2 describe ways of communicating, not of performing.

Answer: 1 — The method prescribed by the proposer

The passage says that where the proposer intimates a particular mode of acceptance in his proposal, it is necessary for the person to whom the proposal is made 'to follow the indicated mode of acceptance'. The mode is therefore set by the proposer, not by the acceptor, so option 2 is exactly the reversal the passage rules out. Options 3 and 4 bring in general legal or trade practice, which the passage never mentions.