The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion (s) logically and definitely follow(s) from the information given in the statements. Statements: Some cats are hens. All hens are goat. Conclusions: Conclusion I: Some hens are cat.
Both conclusions I and II follow
Understanding Syllogism Statements and Conclusions
The question provides two statements and two conclusions based on those statements. We need to determine which of the conclusions logically follow from the given statements, assuming the statements are absolutely true.
Given Statements:
Let's list the statements clearly:
- Statement 1: Some cats are hens.
- Statement 2: All hens are goat.
Given Conclusions:
Now let's look at the conclusions we need to evaluate:
- Conclusion I: Some hens are cat.
- Conclusion II: Some goats are hens.
Analyzing the Syllogism Conclusions
We will analyze each conclusion based on the provided statements using the rules of logic for syllogisms.
Analysis of Conclusion I: Some hens are cat.
Statement 1 says "Some cats are hens". In logic, a statement like "Some A are B" is a specific type of relationship. If "Some cats are hens", it means there is at least one cat that is also a hen. The converse of "Some A are B" is "Some B are A". If some cats are hens, it logically and definitely follows that some hens are cats. There is an overlap between the set of cats and the set of hens, meaning some members of the hen set are also in the cat set.
Therefore, Conclusion I logically follows from Statement 1.
Analysis of Conclusion II: Some goats are hens.
Statement 2 says "All hens are goat". This is a universal positive statement. It means that every single member of the 'hens' group is also a member of the 'goat' group. If "All hens are goat", it implies that the group of hens is completely contained within the group of goats. From a universal positive statement ("All A are B"), we can logically deduce a particular positive statement ("Some B are A"). If all hens are goats, it means that the set of hens is a subset of the set of goats. Because the set of hens is not empty (as per standard syllogism assumptions unless stated otherwise), there are some members in the set of goats that are also hens (specifically, all the hens). Therefore, "Some goats are hens" is a valid deduction.
Therefore, Conclusion II logically follows from Statement 2.
Conclusion Summary
Based on our analysis:
- Conclusion I ("Some hens are cat") follows logically from Statement 1 ("Some cats are hens").
- Conclusion II ("Some goats are hens") follows logically from Statement 2 ("All hens are goat").
Since both conclusions logically and definitely follow from the given statements, the correct answer is that both conclusions I and II follow.
Revision Table: Syllogism Rules
| Statement Type | Example | Valid Conversions/Inferences |
|---|---|---|
| Universal Affirmative (All A are B) | All dogs are mammals. | Some mammals are dogs. (Converse is 'All B are A', which is not always valid) |
| Universal Negative (No A are B) | No cat is a dog. | No dog is a cat. (Simple Converse) All A are not B. (Obverse) |
| Particular Affirmative (Some A are B) | Some students are engineers. | Some engineers are students. (Simple Converse) |
| Particular Negative (Some A are not B) | Some animals are not cats. | No valid simple converse. |
Additional Information: Basic Syllogism Concepts
Syllogisms are a form of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are assumed to be true. In competitive exams, questions often involve analyzing statements about categories and determining which conclusions necessarily follow.
- Statements: These are the initial propositions assumed to be true. They establish relationships between different categories (e.g., cats, hens, goats).
- Conclusions: These are the statements that you must evaluate to see if they are necessarily true based *only* on the information provided in the statements.
- Keywords: Words like "All", "Some", and "No" are crucial as they define the quantity and quality of the relationship between categories.
- Logical Deduction: The process of inferring conclusions directly and unavoidably from the given statements using established rules of logic.
Remember to only use the information given in the statements and avoid bringing in outside knowledge or assumptions about the categories mentioned.
Similar Questions
Read the given statements and conclusions carefully. Assuming that the information given in the statements are true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
1. All colours are reds.
2. Some reds are greens.
3. All greens are dark.
Conclusions:
I. All colours being dark is a possibility
II. Some reds are dark.
III. Some reds are colours.
Read the given statements and conclusions carefully. Assuming that the information given in the statement is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
All chairs are cupboards.
Some chairs are radios.
No chair is piano.
Conclusions:
I. Some radios are cupboards.
II. Some cupboards are not piano.
III. Some radios are not piano.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is ture, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
All aero-planes are cars.
All helicopters are cars.
All cars are scooters.
Conclusions:
1. All helicopters are scooters.
2. Some aero-planes are helicopters.
3. No aero-plane is helicopter.
The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow (s) from the information given in the statements.
Statements:
All books are grapes.
Some grapes are fruits.
Conclusions:
I. No grape is a book.
II. Some grapes are books.The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
Some fans are radio.
All fans are light.
Conclusion I: Some radios are light.
Conclusion II: Some lights are radio.Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some scissors are spoons.
All spoons are plates.
Conclusions:
1. Some plates are spoons.
2. Some spoons are scissors.
3. Some plates are scissors.
Read the given statements and conclusions carefully. Assuming that the information given in the statement is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
No boat is ship.
Some ships are rods.
Conclusions:
I. No boat is rod.
II. Some rods are ships.
III. Some rods are not boats.
The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
Some tents are cones.
All the cones are motels.
Conclusions:
All the motels are cones.
Some tents are motels.The statements below are followed by four conclusions labelled I, II, III and IV. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
No laptop is notebook.
All notebooks are tablets.
Conclusions:
I. No laptop is tablets.
II. No tablets is laptop.
III. Some tablets are notebooks.
IV. All the tablets are notebooks.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some pictures are prizes.
Some prizes are erasers.
Some erasers are helmets.
Conclusions:
I. Some helmets are Prizes.
II. Some erasers are pictures.
III. No helmet is a Prize.
Important Questions from Syllogism
The statements below are followed by conclusions labeled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally Established facts, decide which conclusion(s) logically and definitely follow(s) from the Information, Given in the Statements.
Statements:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
