Two statements are given followed by conclusions numbered 1 and 2. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: 1. Some mammals are animals. 2. All animals are birds. Conclusions: 1. All birds are animals. 2. Some mammals are birds.
Only conclusion 2 follows
Understanding Syllogism Statements and Conclusions
Syllogism questions test your ability to draw logical conclusions from given statements, assuming the statements are true regardless of common knowledge. We are given two statements and two conclusions about mammals, animals, and birds.
Analyzing the Given Syllogism Statements
Let's look at the provided statements:
- Statement 1: Some mammals are animals.
- Statement 2: All animals are birds.
In syllogism, these statements establish relationships between different categories: mammals, animals, and birds.
Evaluating the Given Conclusions
We need to determine which of the following conclusions logically follow from the statements:
- Conclusion 1: All birds are animals.
- Conclusion 2: Some mammals are birds.
Step-by-Step Logical Deduction
Let's evaluate each conclusion based on the given statements.
Analysis of Conclusion 1: All birds are animals.
- Statement 2 says, "All animals are birds". This means the set of animals is entirely contained within the set of birds.
- Conclusion 1 says, "All birds are animals". This would mean the set of birds is entirely contained within the set of animals.
- The relationship "All A are B" does not automatically imply "All B are A". For example, "All dogs are mammals" is true, but "All mammals are dogs" is false.
- Therefore, Conclusion 1 ("All birds are animals") does not logically follow from Statement 2 ("All animals are birds").
Analysis of Conclusion 2: Some mammals are birds.
- Statement 1 says, "Some mammals are animals". This means there is at least one mammal that is also an animal.
- Statement 2 says, "All animals are birds". This means every single animal is also a bird.
- Now, let's combine these. We know there are some mammals that are animals (from Statement 1). Since all animals are birds (from Statement 2), those specific mammals that are animals must also be birds.
- Therefore, if some mammals are animals, and all animals are birds, it logically follows that some mammals are birds.
- Conclusion 2 ("Some mammals are birds") logically follows from the statements.
Summary of Conclusions
Based on our analysis:
- Conclusion 1: All birds are animals - Does not follow.
- Conclusion 2: Some mammals are birds - Follows.
Thus, only Conclusion 2 logically follows from the given statements.
Revision Table: Syllogism Basics
| Type of Statement | Relationship | Example | Converse (usually does not follow) |
|---|---|---|---|
| All A are B | A ⊆ B | All cats are mammals. | All mammals are cats. (False) |
| Some A are B | A ∩ B ≠ ∅ | Some students are athletes. | Some athletes are students. (Follows - if A ∩ B ≠ ∅, then B ∩ A ≠ ∅) |
| No A are B | A ∩ B = ∅ | No fish are birds. | No birds are fish. (Follows - if A ∩ B = ∅, then B ∩ A = ∅) |
Additional Information: Types of Propositions in Syllogism
Statements in syllogism are typically one of four types, often called categorical propositions:
- Universal Affirmative (A): All S are P (e.g., All animals are birds).
- Universal Negative (E): No S are P (e.g., No fish are birds).
- Particular Affirmative (I): Some S are P (e.g., Some mammals are animals).
- Particular Negative (O): Some S are not P (e.g., Some mammals are not birds).
Understanding these types helps in analyzing the relationships and drawing valid logical conclusions.
Similar Questions
Two statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All teachers are engineers.
All clerks are teachers.
Conclusions:
I. Some engineers are clerks.
II. Some teachers are clerks.
III. Some clerks are not engineers.
Two statements are given followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All keys are locks.
All locks are handles.
Conclusions:
I. Some locks are keys.
II. Some handles are keys.
Three Statements are given followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All switches are fans.
No heater is a fan.
Some wires are heaters.
Conclusions:
I. Some wires are fans.
II. No switch is a heater.
III. No wire is a switch.
Three statements are given followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All H are G.
All V are H.
Some V are I.
Conclusions:
I. At least some G are I.
II. All I being H is a possibility.
Three Statements are given followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements :
Some beds are chairs.
Some chairs are tables.
All tables are cupboards.
Conclusions :
I. Some tables are beds.
II. Some cupboards are chairs.
III. Some cupboards are beds.
Read the given statement(s) 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 statement(s).
Statements :
Some ceilings are beds.
No bed is an apple.
All dogs are beds.
Conclusions :
I. Some ceilings being dogs is a possibility.
II. No dog is an apple.
III. All beds are dogs.
IV. No ceiling is an apple.
Three statements are given followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements :
No crow is a monkey.
All monkeys are turtles.
No turtle is a snail.
Conclusions :
I. Some snails being crows is a possibility.
II. No turtle is a crow.
Three statements are given followed by four conclusions numbered I, II, III and IV. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All laptops are desktops.
All desktops are printers.
Some printers are monitors.
Conclusions:
I. Some laptops are monitors.
II. Some monitors are desktops.
III. All laptops are printers.
IV. Some monitors are printers.
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 fans are hammers.
All hammers are fishes.
Conclusions:
I. No fans are fishes.
II. Some fans are fishes.
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:
Some fans are coolers.
All coolers are equipment.
Some equipment are mobiles.
Conclusions:
I. Some equipments are fans.
II. Some mobiles are fans.
III. No equipment is fan and cooler both
Important Questions from Conventional Syllogism
In this question, three statements followed by two conclusions numbered I and II have been given. You have to take the given statements to be true even if they seem to be at variance from the commonly facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements: Some flats are apartments.
No apartment is a hall.
Some halls are rooms.
Conclusions: I. At least some rooms are flats.
II. No apartment is a room.
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:
I. Some blue are red.
II. Some green are red.
Conclusions:
I. No blue is green.
II. No red is green.
In the question two statements are given, followed by three conclusions, I, II and III. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statement 1 : Some cars are scooters.
Statement 2 : All scooters are buses.
Conclusion I : Some scooters are cars.
Conclusion II : Some buses are cars.
Conclusion III : All cars are buses.
Read the given statements and conclusions carefully. Assuming that the information in the statement is true even if they appear to be at variance with commonly known facts, choose the conclusion that logically follows from the statement beyond reasonable doubt.
Statement:-
1. Some dogs are cats.
2. All cats are birds.
Conclusion:-
1. Some dogs are birds.
2. No cat is dog.
In each question below are given three statements followed by two conclusions numbered I and II. You have to take the two/three given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statement:
Some mobiles are laptops.
No laptop is computer.
All phones are computer.
Conclusion:
I. At least some mobiles are computer.
II. At least some phone are laptops.
