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: Some vehicles are helicopters. All helicopters are cars. Conclusions: I. All vehicles are cars. II. Some vehicles are cars.
Only conclusion II follows
Syllogism Logic: Analyzing Statements and Conclusions about Vehicles, Helicopters, and Cars
This question requires us to analyze two given statements and determine which of the two conclusions logically follows based on those statements, even if the statements contradict common knowledge. This type of problem is known as syllogism or logical reasoning.
Understanding the Statements
Let's break down the statements:
- Statement 1: Some vehicles are helicopters. This tells us there is an overlap between the category of "vehicles" and the category of "helicopters". Not all vehicles are helicopters, and not all helicopters are necessarily vehicles (though in the real world, they are, but we must stick to the statements).
- Statement 2: All helicopters are cars. This is a strong statement. It means the entire category of "helicopters" is included within the category of "cars". Anything that is a helicopter must also be a car, according to this statement.
Combining the Statements
We can visualize these statements or combine them logically. Since Statement 1 says some vehicles are helicopters, and Statement 2 says all helicopters are cars, the vehicles that are identified as helicopters in Statement 1 must also be cars (because all helicopters are cars). Therefore, there is a group of vehicles that are also cars.
We can represent this using Venn diagrams:
- Draw a circle for "Vehicles".
- Draw a circle for "Helicopters" that partially overlaps with the "Vehicles" circle (to show "Some vehicles are helicopters").
- Draw a circle for "Cars" that completely encloses the "Helicopters" circle (to show "All helicopters are cars").
From this diagram, the area where "Vehicles" and "Helicopters" overlap is inside the "Cars" circle. This means the vehicles in that overlapping region are also cars.
Evaluating the Conclusions
Now let's examine each conclusion based on our combined understanding:
- Conclusion I: All vehicles are cars.
Does the diagram or logic show that every single vehicle is within the circle of cars? No. The statements only guarantee that the vehicles that are helicopters are cars. There might be other vehicles (like trucks or motorcycles) that are not helicopters and are not necessarily cars according to these statements. Therefore, this conclusion does not logically follow.
- Conclusion II: Some vehicles are cars.
Does the diagram or logic show that there is at least one vehicle that is also a car? Yes. We know from Statement 1 that some vehicles are helicopters. We know from Statement 2 that all helicopters are cars. Therefore, the specific vehicles that are helicopters are also cars. This confirms that "some vehicles" are indeed "cars". This conclusion logically follows.
Conclusion
Based on the logical deduction from the given statements, only Conclusion II follows.
Revision Table: Syllogism Key Concepts
| Term | Explanation | Example based on question |
|---|---|---|
| Statement | A premise assumed to be true for the purpose of the argument. | Some vehicles are helicopters. All helicopters are cars. |
| Conclusion | A proposition that is claimed to follow logically from the statements. | All vehicles are cars. Some vehicles are cars. |
| Syllogism | A form of logical reasoning where a conclusion is drawn from two statements. | The entire problem structure. |
| "Some" | Indicates at least one, but not necessarily all. Represents partial overlap. | "Some vehicles are helicopters" — implies there's an overlap. |
| "All" | Indicates every member of one category is part of another. Represents inclusion. | "All helicopters are cars" — the 'Helicopters' set is inside the 'Cars' set. |
Additional Information: Solving Syllogism Problems
Syllogism problems test your ability to derive logical conclusions from given statements. Here are some common methods and points to remember:
- Stick to the Statements: Only use the information provided in the statements. Do not use your knowledge of the real world if it contradicts the statements.
- Venn Diagrams: Drawing Venn diagrams is a popular and effective way to visualize the relationships between categories described in the statements.
- Rules of Syllogism: There are formal rules for valid syllogisms, but understanding the relationships (inclusion, exclusion, partial overlap) is often sufficient for basic problems.
- Keywords like 'All', 'Some', 'No': Pay close attention to these quantifiers as they define the relationship between categories. 'Some' means at least one, and could mean all in some cases, but doesn't guarantee 'all'. 'All' means every single one. 'No' means complete exclusion.
- Possibility vs. Definite Conclusion: A conclusion must *definitely* follow from the statements to be considered valid. If a conclusion is only *possible* but not guaranteed, it does not logically follow.
Similar Questions
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:
Some curtains are pillows.
No pillow is a bedsheet.
Some curtains are bedsheets.
Conclusions:
I. No curtain is a bedsheet.
II. No pillow is a curtain.
III. Some bedsheets are curtains.
IV. Some pillows are curtains.
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 dates are cashews.
All cashews are raisins.
Some raisins are almonds.
Conclusions:
I. All almonds being dates is a possibility.
II. All dates are raisins.
III. No cashew is an almond.
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 plants are flowers.
Some flowers are fruits.
All flowers are gardens.
Conclusions:
I. Some gardens are plants.
II. Some fruits are gardens.
III. Some gardens are flowers.
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.
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 classrooms are schools.
No school is a park.
All houses are parks.
Conclusions:
I. No house is a classroom.
II. No park is a classroom.
III. No school is a house.
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
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 inkpots are kettles.
All utensils are candies.
No kettle is utensil.
Conclusions:
1. Some inkpots are candies.
2. Some kettles are inkpots.
3. Some candies are inkpots.
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 holders are hangers.
All hangers are hammers.
Some hammers are axes.
Conclusions:
I. Some axes are hangers.
II. Some hammers are holders.
III. Some hangers are holders.
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:
Some blankets are quilts.
Some quilts are bedsheets.
Conclusions:
I. All quilts are blankets.
II. All blankets are bedsheets.
Important Questions from Conventional 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:
1. Some flowers are chemicals.
2. Some chemicals are herbs.
Conclusions:
I. No flower is a herb.
II. Some flowers are herbs.
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 students are teachers.
All teachers are professors.
Conclusions:
1. All students are professors.
2. All professors are students.
3. No teacher is a professor.
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 dentists are surgeons.
II. All the surgeons are doctors.
Conclusions:
I. Some dentists are doctors.
II. No surgeons are dentists.
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 at variance with generally established facts. decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
1) Some angers are griefs.
2) Some griefs are loves.
Conclusion:
I. Some griefs are angers.
II. Some loves are griefsThe 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 cows are deer.
Some deer are fishes.
Conclusion:
I. Some cows are fishes.
II. Some fishes are cows.
