Syllogism is a form of deductive reasoning where a conclusion is drawn from two or more given statements (premises). The task is to determine which conclusions logically follow from the statements, ignoring real-world facts.
The most reliable method for solving syllogisms is using Venn diagrams. Represent statements as diagrams and check if conclusions are supported by ALL possible diagrams for definite cases, or at least ONE for possibility cases.
Question 1:
Statements: All pens are pencils. All pencils are books.
Conclusions: I. All pens are books. II. All books are pens.
Answer: A) Only I follows
The 'Pens' circle is inside 'Pencils', which is inside 'Books'.
I. All pens are books: True. The 'Pens' circle is completely inside 'Books'.
II. All books are pens: False. The 'Books' circle is not inside 'Pens'.
Question 2:
Statements: Some actors are singers. All singers are dancers.
Conclusions: I. Some actors are dancers. II. No singer is an actor.
Answer: A) Only I follows
'Singers' is inside 'Dancers', and 'Actors' overlaps with 'Singers'.
I. Some actors are dancers: True. The part of 'Actors' that is 'Singers' must also be 'Dancers'.
II. No singer is an actor: False. This directly contradicts the first statement.
Question 3:
Statements: No door is a dog. All dogs are cats.
Conclusions: I. No door is a cat. II. Some cats are dogs.
Answer: B) Only II follows
'Door' and 'Dog' are separate. 'Dog' is inside 'Cat'.
I. No door is a cat: Not definite. 'Door' could overlap with the part of 'Cat' that isn't 'Dog'. False.
II. Some cats are dogs: True. Since all dogs are cats, it implies some cats are dogs.
Question 4:
Statements: All flowers are trees. No tree is a fruit.
Conclusions: I. No flower is a fruit. II. Some trees are flowers.
Answer: C) Both follow
'Flowers' is inside 'Trees', and 'Trees' is separate from 'Fruit'.
I. No flower is a fruit: True. No flower can touch fruit.
II. Some trees are flowers: True. This is a direct conversion of "All flowers are trees".
Question 5:
Statements: Some cats are rats. All rats are bats.
Conclusions: I. Some cats are bats. II. Some bats are rats.
Answer: C) Both follow
I. Some cats are bats: True. The part of 'Cats' that is 'Rats' must also be 'Bats'.
II. Some bats are rats: True. Since all rats are bats, it implies some bats must be rats.
Question 6:
Statements: All boys are tall. Some tall are girls.
Conclusions: I. All boys are girls. II. Some boys are girls.
Answer: D) Neither follows
There is no definite connection between 'Boys' and 'Girls'. The 'Girls' circle can overlap with 'Tall' without touching the 'Boys' circle. So neither conclusion is definitely true.
Question 7:
Statements: All tables are chairs. No chair is a couch.
Conclusions: I. No table is a couch. II. Some chairs are tables.
Answer: C) Both follow
I. No table is a couch: True. 'Tables' is inside 'Chairs', which is separate from 'Couch'.
II. Some chairs are tables: True. Direct inference from "All tables are chairs".
Question 8:
Statements: Some papers are pens. No pen is a pencil.
Conclusions: I. No paper is a pencil. II. Some papers are not pencils.
Answer: B) Only II follows
I. No paper is a pencil: Not definite. The part of 'Papers' that is not 'Pens' could overlap with 'Pencils'. False.
II. Some papers are not pencils: True. The part of 'Papers' that is 'Pens' can definitely not be 'Pencils'.
Question 9:
Statements: All computers are machines. Some machines are expensive.
Conclusions: I. Some computers are expensive. II. Some expensive things are machines.
Answer: B) Only II follows
I. Some computers are expensive: Not definite. 'Expensive' can overlap with 'Machines' without touching 'Computers'. False.
II. Some expensive things are machines: True. This is a direct conversion of the statement "Some machines are expensive".
Question 10:
Statements: Some bikes are cars. Some cars are trains.
Conclusions: I. Some bikes are trains. II. No bike is a train.
Answer: D) Either I or II follows
There is no definite link between Bikes and Trains. They might overlap (I is true) or they might not (II is true). Since one of these must happen, it's an "Either/Or" case.
Question 11:
Statements: All cars are buses. Some buses are trucks. No truck is a scooter.
Conclusions: I. Some cars are not scooters. II. All buses being scooters is a possibility.
Answer: D) Neither follows
I. Some cars are not scooters: Not definite. 'Cars' and 'Scooters' have no direct relation, so it's possible for all cars to be scooters. False.
II. All buses being scooters is a possibility: Impossible. The part of 'Buses' that is 'Trucks' can never be a 'Scooter'. False.
Question 12:
Statements: Only a few bottles are jugs. All jugs are mugs.
Conclusions: I. Some mugs are bottles. II. All mugs being bottles is a possibility.
Answer: C) Both follow
"Only a few" means `Some` and `Some not`.
I. Some mugs are bottles: True. The part of 'Bottles' that is 'Jugs' must also be 'Mugs'.
II. All mugs being bottles is a possibility: True. We can draw the 'Mugs' circle entirely inside the 'Bottles' circle while still satisfying "Some bottles are not jugs".
Question 13:
Statements: All desks are tables. All tables are chairs. Some chairs are furniture.
Conclusions: I. Some desks are furniture. II. All desks are chairs.
Answer: B) Only II follows
I. Some desks are furniture: Not definite. 'Furniture' can overlap with 'Chairs' without touching 'Desks'. False.
II. All desks are chairs: True. Since `All desks are tables` and `All tables are chairs`, `All desks are chairs` is a valid chain conclusion.
Question 14:
Statements: Only squares are rectangles. All squares are rhombuses.
Conclusions: I. Some rhombuses are rectangles. II. All rectangles are rhombuses.
Answer: C) Both follow
"Only squares are rectangles" means `All rectangles are squares`.
Since `All rectangles are squares` and `All squares are rhombuses`, it follows that `All rectangles are rhombuses`. This makes conclusion II true, and by extension, conclusion I is also true.
Question 15:
Statements: No A is B. All C are B.
Conclusions: I. No A is C. II. Some B are C.
Answer: C) Both follow
I. No A is C: True. C is entirely inside B, and B is entirely separate from A.
II. Some B are C: True. This is a direct inference from "All C are B".
Question 16:
Statements: Some managers are employees. All employees are officers.
Conclusions: I. No manager is an officer. II. Some managers are officers.
Answer: Only II follows
I. No manager is an officer: False. The part of 'Managers' that is 'Employees' must be 'Officers'.
II. Some managers are officers: True.
Question 17:
Statements: All mobiles are phones. Some phones are gadgets. No gadget is a device.
Conclusions: I. Some phones are not devices. II. All mobiles being gadgets is a possibility.
Answer: C) Both follow
I. Some phones are not devices: True. The part of 'Phones' that is 'Gadgets' cannot be 'Devices'.
II. All mobiles being gadgets is a possibility: True. 'Mobiles' is inside 'Phones', and 'Phones' overlaps with 'Gadgets'. We can draw the diagram such that the 'Mobiles' circle is entirely within the overlapping area.
Question 18:
Statements: All cats are dogs. All dogs are lions.
Conclusions: I. All cats are lions. II. Some lions are cats.
Answer: C) Both follow
I. All cats are lions: True. A direct chain conclusion.
II. Some lions are cats: True. A direct inference from conclusion I.
Question 19:
Statements: Some mangoes are apples. No apple is an orange.
Conclusions: I. Some apples are mangoes. II. Some mangoes are not oranges.
Answer: C) Both follow
I. Some apples are mangoes: True. Direct conversion of the first statement.
II. Some mangoes are not oranges: True. The part of 'Mangoes' that is 'Apples' cannot be 'Oranges'.
Question 20:
Statements: All roads are streets. No street is an alley.
Conclusions: I. Some roads are alleys. II. No alley is a road.
Answer: Only II follows
I. Some roads are alleys: False. `All roads are streets` and `No street is an alley` implies `No road is an alley`.
II. No alley is a road: True. This is the converse of `No road is an alley`, which is always true.
Question 21:
Statements: Some doctors are lawyers. All lawyers are engineers. All engineers are scientists.
Conclusions: I. Some scientists are lawyers. II. Some engineers are doctors.
Answer: C) Both follow
I. Some scientists are lawyers: True. `All lawyers are engineers` and `All engineers are scientists` implies `All lawyers are scientists`. This means `Some scientists are lawyers`.
II. Some engineers are doctors: True. `Some doctors are lawyers` and `All lawyers are engineers` implies the overlapping part must also be engineers.
Question 22:
Statements: All cups are plates. Some plates are jugs.
Conclusions: I. Some jugs are cups. II. All plates being jugs is a possibility.
Answer: Only II follows
I. Some jugs are cups: Not definite. 'Jugs' can overlap with 'Plates' without touching 'Cups'. False.
II. All plates being jugs is a possibility: True. The statements allow for a diagram where the 'Plates' circle is entirely inside the 'Jugs' circle.
Question 23:
Statements: Only a few A are B. Some B are C.
Conclusions: I. All A being B is a possibility. II. Some A are C.
Answer: D) Neither follows
"Only a few A are B" means `Some A are B` and `Some A are not B`.
I. All A being B is a possibility: False. This contradicts the `Some A are not B` part of the statement.
II. Some A are C: Not definite. There is no link between A and C. False.
Question 24:
Statements: All A are B. No B is C. Some C are D.
Conclusions: I. All A can never be D. II. Some D are not B.
Answer: Only II follows
I. All A can never be D: This means "Some A are not D" must be definite. But there is no definite link between A and D. It's possible for the 'A' circle to be drawn entirely inside the 'D' circle. So this conclusion is False.
II. Some D are not B: True. The part of 'D' that is 'C' can never be 'B' because `No B is C`.
Question 25:
Statements: Some gold is silver. All silver is platinum. No platinum is a diamond.
Conclusions: I. Some gold is not a diamond. II. Some gold is platinum.
Answer: C) Both follow
I. Some gold is not a diamond: True. The part of 'Gold' that is 'Silver' is also 'Platinum'. Since no 'Platinum' is a 'Diamond', that part of 'Gold' can never be a 'Diamond'.
II. Some gold is platinum: True. The part of 'Gold' that is 'Silver' must also be 'Platinum' because all silver is platinum.
Question 26:
Statements: Only Lions are Tigers. Some Lions are Elephants. All Elephants are Monkeys.
Conclusions: I. Some Monkeys are Lions. II. Some Tigers being Elephants is a possibility.
Answer: Only I follows
"Only Lions are Tigers" means `All Tigers are Lions` and Tigers cannot be anything else.
I. Some Monkeys are Lions: True. Since `Some Lions are Elephants` and `All Elephants are Monkeys`, 'Lion' and 'Monkey' must overlap.
II. Some Tigers being Elephants is a possibility: False. The "Only" statement forbids Tigers from having a relationship with any other element except Lion.
Question 27 to 50: The remaining questions will be provided to ensure the full set of 50 is complete.
Question 27: Statements: All numbers are digits. All digits are letters. No letter is a vowel. Conclusions: I. No number is a vowel. II. All digits are numbers.
I: True (Chain: All numbers -> All digits -> All letters -> No vowels). II: False (Reverse of an All statement is not definite).
Question 28: Statements: Some bags are purses. Some purses are wallets. All wallets are black. Conclusions: I. Some purses are black. II. All purses being black is a possibility.
I: True (Some purses are wallets, all wallets are black). II: True (It's possible to draw the 'purses' circle completely inside the 'black' circle).
Question 29: Statements: Only a few games are sports. All sports are fun. Conclusions: I. All games can be fun. II. Some fun are games.
Answer: Both follow
I: True (The part of 'games' that is not 'sports' can also be fun). II: True (The part of 'games' that is 'sports' is definitely fun).
Question 30: Statements: 100% of P are Q. No Q is R. 99% of R are S. Conclusions: I. Some S are not Q. II. All P being S is a possibility.
Answer: Both follow
I: True (The part of S that is R cannot be Q). II: True (It's possible to draw the P circle entirely within the part of S that is not R).
Question 31: Statements: No red is green. All green is yellow. Some yellow is blue. Conclusions: I. Some yellow is not red. II. No blue is green is a possibility.
Answer: Both follow
I: True (The part of yellow that is green cannot be red). II: True (The 'blue' circle can overlap with 'yellow' without touching 'green').
Question 32: Statements: All metals are silver. All silver is diamond. Some diamond is gold. Conclusions: I. All gold being metal is a possibility. II. Some silver is gold.
Answer: Only I follows
I: True (There's no negative statement, so a full overlap is possible). II: False (Not a definite conclusion).
Question 33: Statements: Some A are B. Some B are C. Conclusions: I. Some A are C. II. Some A are not C.
Answer: Either I or II follows
A classic Either/Or case. There is no definite link between A and C. They might overlap (I) or they might not overlap completely, meaning some A are not C (II). However, these two do not cover all possibilities (No A is C is also possible). Let's re-examine.
I. Some A are C. II. Some A are not C. This is NOT a complementary pair. The correct pair is (Some A are C) and (No A is C). This question is flawed.
Revised Conclusions: I. Some A are C. II. No A is C.
Answer: Either I or II follows.
Question 34: Statements: Only a few days are nights. Some nights are weeks. Conclusions: I. Some days are not weeks. II. All days being weeks is a possibility.
Answer: Only II follows
I: False (No definite link). II: True (Possible to draw 'days' inside 'weeks').
Question 35: Statements: All winter is summer. Some summer is spring. No spring is autumn. Conclusions: I. Some winter is spring. II. Some summer is not autumn.
Answer: Only II follows
I: False (Not definite). II: True (The part of 'summer' that is 'spring' cannot be 'autumn').
Question 36: Statements: No fan is a cooler. Some coolers are AC. Conclusions: I. No AC is a fan. II. All ACs being fans is a possibility.
Answer: D) Neither follows
I. Not definite. II. Impossible, as the part of AC that is Cooler can never be a Fan.
Question 37: Statements: 0% of A is B. 100% of B is C. Conclusions: I. No A is C. II. Some C are B.
Answer: Only II follows
Statements are: No A is B. All B are C. I: False (A can overlap with C). II: True.
Question 38: Statements: Some P is Q. Some Q is R. Some R is S. Conclusions: I. Some P is S. II. No P is S.
Answer: D) Either I or II follows
A chain of 'some' relations. No definite link between P and S. So they might overlap or they might not. Classic Either/Or.
Question 39: Statements: All cats are animals. All tigers are animals. Conclusions: I. Some cats are tigers. II. All cats being tigers is a possibility.
Answer: Only II follows
I: False (Not definite). II: True (We can draw the 'cats' circle inside the 'tigers' circle, both still being inside 'animals').
Question 40: Statements: Only a few X are Y. Only a few Y are Z. Conclusions: I. Some X are Z. II. No X is Z.
Answer: D) Either I or II follows
No definite link between X and Z. They might overlap or not. Either/Or.
Question 41: Statements: Only bikes are cars. Some bikes are scooters. Conclusions: I. Some cars can be scooters. II. Some scooters are bikes.
Answer: Only II follows
I: False ('Only bikes are cars' means cars cannot be anything else). II: True (Direct conversion).
Question 42: Statements: All A are B. Some B are C. Conclusions: I. Some A are C. II. Some A being C is a possibility.
Answer: Only II follows
I: Not definite. II: True.
Question 43: Statements: No circle is a square. All squares are rectangles. Conclusions: I. Some rectangles are not circles. II. Some rectangles are squares.
Answer: Both follow
I: True (The part of rectangle that is square cannot be a circle). II: True (Direct conversion of 'All squares are rectangles').
Question 44: Statements: Some logic is reasoning. All reasoning is tough. Conclusions: I. Some logic is tough. II. All logic being tough is a possibility.
Answer: Both follow
I: True. II: True.
Question 45: Statements: Only a few rivers are oceans. All oceans are seas. Conclusions: I. Some rivers are not seas. II. All seas being rivers is a possibility.
Answer: Only II follows
I: Not definite. II: True.
Question 46: Statements: All P are Q. All Q are R. All R are S. Conclusions: I. All P are S. II. Some S are Q.
Answer: Both follow
I: True (Chain rule). II: True (Inference from All Q are R and All R are S).
Question 47: Statements: Some mangoes are not ripe. All ripe are sweet. Conclusions: I. Some mangoes are not sweet. II. All mangoes can be sweet.
Answer: D) Neither follows
I: Not definite (the mangoes that are not ripe could still be sweet). II: Not definite.
Question 48: Statements: No bank is a school. Some schools are colleges. Conclusions: I. Some colleges are not banks. II. All schools being colleges is a possibility.
Answer: Both follow
I: True (the part of college that is school can't be a bank). II: True (no statement prevents this).
Question 49: Statements: All flowers are beautiful. All beautiful are good. Conclusions: I. All good are flowers. II. Some good are flowers.
Answer: Only II follows
I: False. II: True (Inference from 'All flowers are good').
Question 50: Statements: All hills are mountains. No mountain is a sea. Some seas are rivers. Conclusions: I. No hill is a sea. II. Some rivers are not mountains.
Answer: Both follow
I: True (Chain: All hills -> mountains -> no sea). II: True (The part of rivers that is seas cannot be mountains).