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: All rectangles are trapezium. All trapeziums are parallelogram. No parallelogram is circle. Conclusions: I) No rectangle is circle. II) No trapezium is circle. III) All rectangles are parallelogram.
This question tests your understanding of deductive reasoning and syllogisms. Let's analyze the given statements and conclusions:
Statements:
- All rectangles are trapeziums.
- All trapeziums are parallelograms.
- No parallelogram is a circle.
Conclusions:
- I) No rectangle is a circle. This is true. Since all rectangles are trapeziums, and all trapeziums are parallelograms, and no parallelogram is a circle, it follows that no rectangle is a circle. This is a valid deductive inference.
- II) No trapezium is a circle. This is also true. Given that all trapeziums are parallelograms, and no parallelogram is a circle, it logically follows that no trapezium is a circle.
- III) All rectangles are parallelograms. This is true. Since all rectangles are trapeziums, and all trapeziums are parallelograms, it directly implies that all rectangles are parallelograms. This demonstrates the transitive property of logical inference.
Therefore, all conclusions I, II, and III logically follow from the given statements.
In summary: The problem uses a series of categorical syllogisms. By applying the rules of deductive reasoning and tracing the relationships between the categories (rectangles, trapeziums, parallelograms, circles), we can confirm the validity of each conclusion. The key is understanding that if A is a subset of B, and B is a subset of C, then A is also a subset of C. Similarly, if no members of C are members of D, and B is a subset of C, then no members of B are members of D. This solution systematically applies these logical principles to arrive at the correct answer.
Similar Questions
- All flowers are plants. Some plants are flowering plants. Which conclusion is logically valid?
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 f act s, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some carpenters are singers.
All singers are doctors.
Conclusions:
I. No doctor is a carpenter.
II. Some doctors are singers.
III. Some carpenters are doctors.
Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statement s 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 machines are coolers.
All coolers are robots.
Some microwaves are coolers.
Conclusions:
I. Some coolers are machines.
II. Some robots are machines.
III. No robot is a microwave.
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:
1. All teachers are students.
2. All principal are teachers.
3. Some principals are doctors.
Conclusions:
I. Some students are teachers.
II. No student is a doctor.
III. Some students are principals.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:
1. All apples are mangoes.
2. Some bananas are mangoes.
Conclusions:
I. Some mangoes are bananas.
II. Some mangoes are apples.
III. No mango is an apple.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:
1. No bed is a chair.
2. All tables are beds.
3. No cupboard is a bed.
Conclusions:
I. No table is a chair.
II. No cupboard is a table.
III. Some beds are tables.
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:
1. No city is a district.
2. Some districts are zones.
3. Some zones are states.
Conclusions:
I. Some zones are districts.
II. Some districts are cities.
lII. No state is a zone.
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:
1. Some tables are chairs.
2. Some chairs are beds.
3. All beds are goods.
Conclusions:
I. Some chairs are goods.
Il. Some goods are not beds.
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:
No man is engineer.
No engineer is driver.
Some drivers are shop-keepers.
Conclusions:
1. Some men are drivers.
2. No shop-keepers are engineer.
3. Some shop-keepers are not engineers.
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.
Important Questions from Syllogism
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 students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
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:
No creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
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 actors are choreographers.
All choreographers are producers.
Not a single producer is a director.
Conclusions:
I. Some actors are directors.
II. Not a single actor is a director.
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 :
1. All flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
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:
All rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
