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
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.
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.
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.
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.
