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 buses are cars. No jeep is a car. Conclusions: I. No car is a jeep. II. No jeep is a bus.
Both conclusions I and II follows.
Solving the Logic Puzzle: Statements and Conclusions
Let's carefully analyze the given statements and conclusions to determine which ones logically follow.
Understanding the Statements
We are given two statements:
- Statement 1: All buses are cars. This means the set of 'buses' is completely contained within the set of 'cars'.
- Statement 2: No jeep is a car. This means the set of 'jeeps' and the set of 'cars' have absolutely no overlap. They are mutually exclusive.
Analyzing the Conclusions
Now let's examine each conclusion based on the statements:
- Conclusion I: No car is a jeep.
This conclusion is the converse of Statement 2 ("No jeep is a car"). In logic, the statement "No A is B" is logically equivalent to "No B is A". If there is no overlap between jeeps and cars (Statement 2), then there is also no overlap between cars and jeeps. Therefore, Conclusion I logically follows from Statement 2.
- Conclusion II: No jeep is a bus.
We know from Statement 1 that all buses are cars. This means every single bus is also a car. We also know from Statement 2 that no jeep is a car. Since buses are a type of car, and jeeps have no relationship with cars, jeeps cannot have any relationship with buses either. If jeeps cannot be cars, and buses are cars, then jeeps cannot be buses. Therefore, Conclusion II logically follows from the combination of Statement 1 and Statement 2.
Synthesizing the Findings
Based on our analysis:
- Conclusion I ("No car is a jeep") follows directly from Statement 2.
- Conclusion II ("No jeep is a bus") follows from the combined logic of Statement 1 and Statement 2.
Both conclusions are logically derived from the given statements.
Final Decision on Conclusions
Both Conclusion I and Conclusion II logically follow from the given statements.
Revision Table: Key Concepts in Syllogism
| Term | Explanation | Example (based on statement "All A are B") |
|---|---|---|
| Statement | A proposition given as true. | All buses are cars. |
| Conclusion | A proposition derived logically from the statements. | No car is a jeep. |
| Syllogism | A type of logical argument where a conclusion is derived from two statements. | Statements → Conclusion |
| Conversion (of E proposition) | Swapping subject and predicate in a "No A is B" statement preserves truth. | "No jeep is a car" is equivalent to "No car is a jeep". |
Additional Information: Deductive Reasoning
This problem is an example of deductive reasoning, specifically a form of syllogism. In deductive reasoning, if the premises (statements) are true, the conclusion that follows must also be true. Unlike inductive reasoning which moves from specific observations to general conclusions, deductive reasoning moves from general statements to specific conclusions.
Venn diagrams can be a helpful tool for visualizing these relationships:
- Statement 1: A circle for 'Buses' drawn completely inside a larger circle for 'Cars'.
- Statement 2: A third circle for 'Jeeps' drawn completely separate from the 'Cars' circle.
Looking at this diagram:
- The 'Cars' circle and 'Jeeps' circle do not touch, confirming "No car is a jeep" (Conclusion I).
- The 'Buses' circle is inside 'Cars', and 'Jeeps' is separate from 'Cars', so 'Jeeps' must also be separate from 'Buses', confirming "No jeep is a bus" (Conclusion II).
Understanding these basic logical structures helps in solving various reasoning problems in exams.
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.
