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 tasks are jobs. No job is a duty. Conclusions I. All tasks can never be duties. II. Some tasks are duties.
Only conclusion I follows
Understanding Syllogism: Analyzing Statements and Conclusions
This question requires us to analyze two given statements and determine which of the two conclusions logically follows from them, assuming the statements are true.
Let's break down the given information:
- Statements:
- Statement 1: Some tasks are jobs.
- Statement 2: No job is a duty.
- Conclusions:
- Conclusion I: All tasks can never be duties.
- Conclusion II: Some tasks are duties.
To solve this type of logical reasoning problem, we can use methods like Venn diagrams or simply analyze the relationships established by the statements.
Analyzing the Syllogism Statements
Let's look at what each statement tells us:
- Statement 1: "Some tasks are jobs." This means there is an overlap between the category of 'tasks' and the category of 'jobs'. A certain portion of 'tasks' falls under the category of 'jobs'.
- Statement 2: "No job is a duty." This establishes a complete separation between the category of 'jobs' and the category of 'duties'. Nothing that is a 'job' can also be a 'duty'.
Evaluating the Conclusions Based on Statements
Now, let's examine each conclusion in light of the statements.
Conclusion I: All tasks can never be duties.
This conclusion claims it is impossible for all tasks to be duties. Let's see if this is supported by the statements.
From Statement 1, we know that there are some tasks that are also jobs.
From Statement 2, we know that nothing that is a job can be a duty.
Combining these two pieces of information:
- There exists a set of things which are both tasks and jobs (from Statement 1).
- Anything that is a job cannot be a duty (from Statement 2).
Therefore, the set of things that are both tasks and jobs cannot be duties. This means that at least some tasks (the ones that are jobs) cannot be duties.
If some tasks cannot be duties, then it is impossible for *all* tasks to be duties. The statement "All tasks can never be duties" is equivalent to saying "It is impossible for all tasks to be duties". Since we have identified a portion of tasks that cannot be duties, this conclusion logically follows.
Conclusion II: Some tasks are duties.
This conclusion claims that there is an overlap between the category of 'tasks' and the category of 'duties'.
We know "Some tasks are jobs" and "No job is a duty". The tasks that are jobs cannot be duties.
What about the tasks that are *not* jobs? The statements provide no information whatsoever about the relationship between the tasks that are not jobs and the category of duties.
It is possible that some tasks that are not jobs are duties. It is also possible that no tasks that are not jobs are duties. Since the statements do not guarantee that there is *any* overlap between tasks and duties, Conclusion II does not logically follow.
Summary of Conclusions
- Conclusion I: All tasks can never be duties. - Logically Follows.
- Conclusion II: Some tasks are duties. - Does Not Logically Follow.
Final Decision
Based on the analysis of the statements, only Conclusion I logically follows.
| Statement/Conclusion | Relationship | Logical Follows? |
|---|---|---|
| Statement 1: Some tasks are jobs. | Tasks & Jobs overlap. | N/A (Premise) |
| Statement 2: No job is a duty. | Jobs & Duties are separate. | N/A (Premise) |
| Conclusion I: All tasks can never be duties. | Impossible for all Tasks to be Duties. | Yes |
| Conclusion II: Some tasks are duties. | Tasks & Duties overlap. | No (Not guaranteed) |
Revision Table: Key Concepts
| Concept | Explanation |
|---|---|
| Syllogism | A form of deductive reasoning where a conclusion is drawn from two or more premises. |
| Statements (Premises) | The initial propositions assumed to be true for the purpose of logical deduction. |
| Conclusions | Propositions that are tested to see if they logically follow from the statements. |
| "Some" relationship | Indicates at least one instance of overlap between two categories. |
| "No" relationship | Indicates complete separation between two categories. |
| "Can never be" | Indicates logical impossibility based on the premises. |
Additional Information: Deductive Logic and Syllogisms
Syllogisms are a fundamental part of deductive logic. In deductive logic, if the premises (statements) are true, the conclusion that logically follows must also be true. The task in these problems is to determine what *must* be true given the statements, not what *might* be true.
Venn diagrams can be a helpful tool to visualize the relationships described in the statements. For "Some A are B", you'd draw two overlapping circles for A and B, shading the overlapping region to indicate existence. For "No B is C", you'd draw separate circles for B and C. By combining these diagrams, you can see if the conclusions represent a relationship that is always true based on the drawing.
In this problem:
- The 'Jobs' circle is separate from the 'Duties' circle.
- The 'Tasks' circle overlaps with the 'Jobs' circle.
This visually shows that the portion of the 'Tasks' circle that is inside the 'Jobs' circle cannot extend into the 'Duties' circle because the 'Jobs' circle avoids the 'Duties' circle entirely. Therefore, it is impossible for the entire 'Tasks' circle to be inside the 'Duties' circle, confirming Conclusion I. The diagram does not force any part of the 'Tasks' circle (specifically, the part that is not 'Jobs') to overlap with the 'Duties' circle, so Conclusion II is not guaranteed.
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.
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:
No file is a folder.
Some files are PDFs.
All files are Excel sheets.
Conclusions:
I. Some PDFs are folders.
II. Some Excel sheets are folders.
III. Some PDFs are Excel sheets.
In this question three statements are given followed by three conclusions I, II and III. You have to consider the three statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion(s) logically follow(s) from the given statements.
Statements:
All photocopiers are computers.
Some computers are laptops.
No laptop is a mobile.
Conclusions:
(I) No computer is a mobile.
(II) Some computers are photocopiers.
(III) All mobiles are photocopiers.
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 paintings are calligraphies.
All sketching are calligraphies .
Conclusions:
I. At least some calligraphies are paintings.
II. No sketching is a painting.
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.
Given below are two statements and two conclusions. Take the statements to be true even if they are at variance with commonly known facts, and decide whether the conclusion(s) follow(s) the given statements.
Statements:
All eyes are noses.
Some noses are lips.
Conclusions:
I. Some noses are eyes.
II. All lips are noses.
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 telescopes are periscopes.
Some telescopes are microscopes.
Some telescopes are kaleidoscopes.
Conclusions:
I. Some kaleidoscopes are telescopes.
II. Some microscopes are kaleidoscopes.
III. Some microscopes are telescopes.
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.
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.
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.
Given below are two statements, Consider these statements to be true even if they seem factuality absurd, Read the conclusions and then decide which of the given conclusions logically follow(s) from the given statements?
Statements :
1. All vases are flowers.
2. No flowers is a plant.
Conclusions :
1. No vases is a plant.
2. Some plant are vases
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. All A are S.
II. No D is A.
Conclusions:
I. Some S are A.
II. All S are D.
III. No A is D.
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. Some land are hard.
II. No stone is land.
Conclusions:
I. Some hard are land.
II. Some stone are hard.
