Loading…
Free Content10 MCQs
Imagine you are a detective trying to solve a puzzle. You get some clues (statements) and you need to figure out what must be true (conclusion). This is exactly what Syllogism is all about! It's a fun way to use logic to find definite answers from given information, even if that information seems a little silly. Mastering Syllogism helps you think clearly and quickly, which is super important for competitive exams.
When you have two statements that are both positive (like 'All' or 'Some'), your definite conclusion will always be positive. A negative conclusion can never be definitely true from only positive statements.
If any statement has the word 'No' or 'Not' in it, it's a negative statement. If you have at least one negative statement, your definite conclusion can be negative. But if all statements are negative, usually no definite positive conclusion is possible.
If a statement says 'Some A are B', you can instantly know that 'Some B are A' is also true. It works both ways for 'Some' statements. This is a quick mental check!
If a statement says 'All A are B', then it's always true that 'Some A are B'. Think of it like this: if you have all mangoes, you definitely have some mangoes!
Just like 'Some', if a statement says 'No A are B', then it's also true that 'No B are A'. If two things are completely separate, it doesn't matter which one you say first.
When two conclusions are individually doubtful (meaning, not definitely true or false), check if they are a 'Some + No' pair or 'All + Some Not' pair, and if they talk about the same two groups (like 'Books' and 'Pens'). If yes, then it's an 'Either/Or' case!
Syllogism is like a fun game of 'What's True?'. You get some sentences called statements. From these statements, you have to decide if other sentences, called conclusions, are definitely true, definitely false, or might be true. The trick is to only use the information given in the statements, even if it feels strange!
There are four main types of statements in Syllogism:
The easiest way to solve Syllogism problems is by drawing pictures called Venn Diagrams. These diagrams help you see how different groups are related.
After drawing the diagrams for all the statements:
Always remember, do not add your own real-world knowledge. Stick to the pictures you draw!
Conversion: All A are B
All A are B → Some B are AConversion: Some A are B
Some A are B → Some B are AConversion: No A are B
No A are B → No B are AConversion: Some A are not B
Some A are not B → Cannot be converted to 'Some B are not A'Either/Or Rule (Type 1)
(Some A are B) + (Some A are not B) = Either/OrEither/Or Rule (Type 2)
(All A are B) + (Some A are not B) = Either/Or| Statement Type | Quantity | Quality | Venn Diagram Hint |
|---|---|---|---|
| All A are B | Universal | Affirmative | Small A circle inside big B circle |
| Some A are B | Particular | Affirmative | A and B circles overlapping |
| No A are B | Universal | Negative | A and B circles separate |
| Some A are not B | Particular | Negative | A circle with a part outside B circle |
Q: Statements: 1. All pencils are pens. 2. Some pens are erasers. Conclusions: I. Some pencils are erasers. II. Some erasers are pens.
Q: Statements: 1. No flower is a tree. 2. All trees are plants. Conclusions: I. No flower is a plant. II. Some plants are trees.
Q: Statements: 1. Some bags are covers. 2. All covers are plastic. Conclusions: I. Some bags are plastic. II. No bag is plastic.
Q: Statements: 1. All tables are chairs. 2. Some chairs are wood. Conclusions: I. Some tables are wood. II. Some tables are not wood.
A traffic rule states: 'All red lights mean stop.' Another rule is: 'Some stops are followed by a green light.' If you see a red light, can you be sure a green light will follow?
In a team, 'All players are good at shooting.' Also, 'Some players are tall.' If someone is good at shooting, does that mean they must be tall?
You have a cookie jar. 'All chocolate cookies have sprinkles.' And 'No oatmeal cookies have sprinkles.' If you pick a cookie with sprinkles, what can you definitely say about it?
In a library, 'Some history books are old.' Also, 'All old books are dusty.' If you find a dusty book, can you say for sure it's a history book?
Statements: 1. All mobiles are phones. 2. Some phones are smart. Conclusions: I. All smart are phones. II. Some mobiles are smart is a possibility.
Statements: 1. No shirt is a pant. 2. All pants are trousers. Conclusions: I. No shirt is a trouser. II. Some trousers are pants.
Statements: 1. All cars are vehicles. 2. All vehicles are wheels. Conclusions: I. All cars are wheels. II. Some wheels are cars.
Statements: 1. Some books are papers. 2. Some papers are pens. Conclusions: I. Some books are pens. II. No book is a pen.
1Statements: 1. All doors are windows. 2. Some windows are open. Conclusions: I. Some doors are open. II. Some windows are doors.
2Statements: 1. No fan is a cooler. 2. All coolers are AC. Conclusions: I. No fan is an AC. II. Some AC are coolers.
3Statements: 1. Some chairs are tables. 2. All tables are wood. Conclusions: I. Some chairs are wood. II. All wood are tables.
4Statements: 1. All animals are mammals. 2. Some mammals are carnivores. Conclusions: I. Some animals are carnivores. II. Some animals are not carnivores.
5Statements: 1. No fruit is a vegetable. 2. All vegetables are green. Conclusions: I. Some green are vegetables. II. No fruit is green.
6Statements: 1. All trees are plants. 2. Some plants are flowers. Conclusions: I. Some trees are flowers. II. Some flowers are plants.
7Statements: 1. Some keys are locks. 2. All locks are security. Conclusions: I. Some keys are security. II. No key is security.
8Statements: 1. All cities are towns. 2. No town is a village. Conclusions: I. No city is a village. II. Some towns are cities.
9Statements: 1. Some pens are pencils. 2. No pencil is an eraser. Conclusions: I. Some pens are not erasers. II. All erasers are pens.
10Statements: 1. All shirts are clothes. 2. Some clothes are white. Conclusions: I. All shirts are white. II. Some white are clothes.
When you have two statements that are both positive (like 'All' or 'Some'), your definite conclusion will always be positive. A negative conclusion can never be definitely true from only positive statements.
If any statement has the word 'No' or 'Not' in it, it's a negative statement. If you have at least one negative statement, your definite conclusion can be negative. But if all statements are negative, usually no definite positive conclusion is possible.
If a statement says 'Some A are B', you can instantly know that 'Some B are A' is also true. It works both ways for 'Some' statements. This is a quick mental check!
If a statement says 'All A are B', then it's always true that 'Some A are B'. Think of it like this: if you have all mangoes, you definitely have some mangoes!
Just like 'Some', if a statement says 'No A are B', then it's also true that 'No B are A'. If two things are completely separate, it doesn't matter which one you say first.
When two conclusions are individually doubtful (meaning, not definitely true or false), check if they are a 'Some + No' pair or 'All + Some Not' pair, and if they talk about the same two groups (like 'Books' and 'Pens'). If yes, then it's an 'Either/Or' case!
All A are B → Some B are ASome A are B → Some B are ANo A are B → No B are A+3 more formulas below