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Imagine you are a little detective solving a small puzzle! In 'Statement & Conclusion' problems, you get some starting facts, called statements. Your job is to figure out what absolutely *must* be true from those facts, without adding any outside ideas. It's like if your mom says, 'All apples are fruits,' you know for sure that 'Some fruits are apples,' right? This skill helps you think clearly and logically, which is super important for exams and even in real life!
When you see 'All A are B', imagine a tiny circle A fully inside a big circle B. For 'Some A are B', draw two circles that just touch a little. For 'No A are B', keep the circles far apart. Quick visuals help your brain 'see' the connections without getting confused.
Assign numbers to words: 'All' is 100 for the first word and 50 for the second. 'Some' is 50 for both. 'No' is 100 for both. 'Some Not' is 50 and 100. For conclusions, combine the '50' numbers. If two statements connect through a common word (called the 'middle term'), their sum must be 150 for a certain conclusion. This helps quickly rule out wrong conclusions without drawing.
If a conclusion is only 'possible' but not 'certain', it's usually wrong in exams. Always ask: 'MUST this be true?' If the answer is 'maybe' or 'sometimes', then it's not a valid conclusion. This trick saves you from falling for tricky options that sound plausible but aren't definite.
If you have only positive statements (like 'All' or 'Some'), you can never get a negative conclusion (like 'No' or 'Some Not'). If the statements say 'All chairs are wood' and 'Some wood is brown', you can't conclude 'No chair is brown' or 'Some chairs are not brown'. This is a quick elimination trick.
Sometimes, two conclusions look opposite, but both could be 'possible' (not 'certain'). If they cover all possibilities for the items and have the same elements (like 'Some A are B' and 'No A are B'), and both are uncertain individually, then an 'Either I or II follows' situation comes up. This is a special case to watch out for.
This topic is like a game where you become a smart detective! You get some sentences called statements. These statements are your clues. Your task is to look at these clues carefully and then decide what other things must be true because of them. These 'must-be-true' things are called conclusions.
Think of it this way: If I tell you, "All dogs can bark," and "My pet is a dog," what *must* be true? You would say, "My pet can bark," right? That's a conclusion! But if you said, "My pet likes bones," that might be true in real life, but the statements didn't tell you that for sure. So, it's not a valid conclusion in this game.
Statements usually come in a few common types:
The biggest rule is: Only accept what is 100% certain! If something is just a possibility, or if you need extra information from outside, then it's not a correct conclusion.
Let's use a simple example: "All pencils are stationery. Some stationery are erasers."
Sometimes drawing simple circles can help you see the connections clearly. This is like making a simple map of your clues.
When you have multiple statements, draw their circles together. Then, see if a conclusion's circle relationship is *forced* by your drawing. If you can draw it in a way that makes the conclusion false, then the conclusion is not 100% certain!
Mastering Statement & Conclusion makes your brain sharper for logical thinking. Practice lots, and you'll become a super logical detective!
All to Some Conversion
If "All A are B" is true, then "Some A are B" and "Some B are A" are true.No to No Conversion
If "No A are B" is true, then "No B are A" is true.Some to Some Conversion
If "Some A are B" is true, then "Some B are A" is true.Chain Rule (All-All)
If "All A are B" and "All B are C", then "All A are C".Negative Conclusion Rule
To get a negative conclusion (No/Some Not), at least one statement must be negative.| Statement Type | Certain Direct Conclusion | Uncertain/Invalid Conclusion |
|---|---|---|
| All A are B | Some A are B; Some B are A | All B are A; No A are B |
| Some A are B | Some B are A | All A are B; No A are B; Some A are not B |
| No A are B | No B are A; Some A are not B; Some B are not A | All A are B; Some A are B |
| Some A are not B | None (no direct certain conversion) | All A are B; No A are B; Some A are B |
Q: Statements: All cats are animals. All animals are living things. Conclusions: I. All cats are living things. II. Some living things are cats.
Q: Statements: Some shirts are blue. No blue is a pant. Conclusions: I. Some shirts are not pants. II. No pant is a shirt.
Q: Statements: All cars are vehicles. Some vehicles are fast. Conclusions: I. All cars are fast. II. Some fast are vehicles.
Q: Statements: No dog is a cat. Some cats are black. Conclusions: I. Some black are not dogs. II. All black are dogs.
Your teacher says, 'All students who finish homework get extra play time.' You know, 'Rahul finished his homework.' What must be true about Rahul?
A shop's sign says, 'All red shirts are 50% off.' You pick up a shirt and see it's red. What must be true about your shirt?
The coach announced, 'Some players selected for the match are fast bowlers.' You know, 'Deepak is a fast bowler.' Does this mean Deepak is definitely selected?
Your grandma says, 'No fruit in this basket is rotten.' You pick an apple from the basket. What must be true about your apple?
Statements: All doors are windows. No window is a wall. Conclusions: I. Some doors are walls. II. No door is a wall.
Statements: Some pens are pencils. Some pencils are erasers. Conclusions: I. Some pens are erasers. II. No pen is an eraser.
Statements: All flowers are beautiful. Some beautiful are roses. Conclusions: I. All flowers are roses. II. Some beautiful are flowers.
Statements: No cow is a bird. All birds are animals. Conclusions: I. Some animals are not cows. II. Some cows are animals.
1Statements: All books are pens. All pens are pencils. Conclusions: I. All books are pencils. II. Some pencils are books.
2Statements: Some chairs are tables. No table is a desk. Conclusions: I. Some chairs are not desks. II. Some desks are not chairs.
3Statements: No fruit is a vegetable. Some vegetables are green. Conclusions: I. No fruit is green. II. Some green are not fruits.
4Statements: Some boys are intelligent. All intelligent are creative. Conclusions: I. Some boys are creative. II. Some creative are boys.
5Statements: All cars are red. All red are vehicles. Conclusions: I. All vehicles are cars. II. Some vehicles are red.
6Statements: Some flowers are plants. No plant is a tree. Conclusions: I. Some flowers are not trees. II. No flower is a tree.
7Statements: All bags are heavy. Some heavy are light. Conclusions: I. All bags are light. II. Some heavy are bags.
8Statements: Some sweets are tasty. Some tasty are sour. Conclusions: I. Some sweets are sour. II. No sweet is sour.
9Statements: All singers are dancers. All dancers are artists. Conclusions: I. All singers are artists. II. Some artists are singers.
10Statements: No shirt is a tie. Some ties are black. Conclusions: I. No shirt is black. II. Some black are not shirts.
When you see 'All A are B', imagine a tiny circle A fully inside a big circle B. For 'Some A are B', draw two circles that just touch a little. For 'No A are B', keep the circles far apart. Quick visuals help your brain 'see' the connections without getting confused.
Assign numbers to words: 'All' is 100 for the first word and 50 for the second. 'Some' is 50 for both. 'No' is 100 for both. 'Some Not' is 50 and 100. For conclusions, combine the '50' numbers. If two statements connect through a common word (called the 'middle term'), their sum must be 150 for a certain conclusion. This helps quickly rule out wrong conclusions without drawing.
If a conclusion is only 'possible' but not 'certain', it's usually wrong in exams. Always ask: 'MUST this be true?' If the answer is 'maybe' or 'sometimes', then it's not a valid conclusion. This trick saves you from falling for tricky options that sound plausible but aren't definite.
If you have only positive statements (like 'All' or 'Some'), you can never get a negative conclusion (like 'No' or 'Some Not'). If the statements say 'All chairs are wood' and 'Some wood is brown', you can't conclude 'No chair is brown' or 'Some chairs are not brown'. This is a quick elimination trick.
Sometimes, two conclusions look opposite, but both could be 'possible' (not 'certain'). If they cover all possibilities for the items and have the same elements (like 'Some A are B' and 'No A are B'), and both are uncertain individually, then an 'Either I or II follows' situation comes up. This is a special case to watch out for.
If "All A are B" is true, then "Some A are B" and "Some B are A" are true.If "No A are B" is true, then "No B are A" is true.If "Some A are B" is true, then "Some B are A" is true.+2 more formulas below