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 desks are trays. Some trays are plates. Some plates are desks. Conclusions: I. All desks are plates. II. All plates are desks. III. Some plates are trays. IV. All trays are desks.
Only conclusion III follows
Analyzing Syllogism Statements about Desks, Trays, and Plates
This question asks us to analyze logical statements about categories (desks, trays, plates) and determine which of the given conclusions logically follow from these statements, assuming the statements are true.
Breaking Down the Given Statements
We are given three statements:
- Some desks are trays.
- Some trays are plates.
- Some plates are desks.
In logic problems like this, the word "Some" means "at least one, and possibly all". However, when drawing conclusions, we must only accept what is *certainly* true based on the statements, not what is possible but not guaranteed. A statement like "Some A are B" implies there is an overlap between the category A and the category B. It does not give us information about *all* of A or *all* of B.
Evaluating the Syllogism Conclusions
We need to check each of the four conclusions against the given statements:
- I. All desks are plates.
- II. All plates are desks.
- III. Some plates are trays.
- IV. All trays are desks.
Step-by-Step Conclusion Analysis
Let's examine each conclusion:
Conclusion I: All desks are plates.
Statement 3 tells us "Some plates are desks". This is equivalent to "Some desks are plates". This confirms there is an overlap between desks and plates. However, the statement "Some desks are plates" does not mean that *all* desks are plates. There could be many desks that are not plates. Therefore, this conclusion does not logically follow from the statements.
Conclusion II: All plates are desks.
Statement 3 says "Some plates are desks". As discussed above, this only guarantees an overlap. It does not mean that *all* plates belong to the category of desks. There could be plates that are not desks. Therefore, this conclusion also does not logically follow.
Conclusion III: Some plates are trays.
Statement 2 is "Some trays are plates". In logic, the statement "Some A are B" is logically equivalent to the statement "Some B are A". If "Some trays are plates," it means there is an overlap between trays and plates. This overlap is the same as saying "Some plates are trays". Therefore, this conclusion logically follows directly from Statement 2.
Conclusion IV: All trays are desks.
Statement 1 is "Some desks are trays". This is equivalent to "Some trays are desks". This statement only confirms an overlap between trays and desks. It does not provide information that *all* trays are desks. There could be trays that are not desks. Therefore, this conclusion does not logically follow.
Identifying the Logically Following Conclusion
Based on our analysis, only Conclusion III, "Some plates are trays", is guaranteed to be true based on the given statements.
Revision Table: Syllogism Concepts
| Statement Type | Meaning/Implication | Example |
|---|---|---|
| All A are B | All members of category A are also members of category B (A is a subset of B). | All dogs are mammals. |
| No A are B | There is no overlap between categories A and B. | No cats are dogs. |
| Some A are B | There is at least one member common to both category A and category B (overlap exists). Does NOT mean 'only some' or 'not all'. | Some students are athletes. |
| Some A are not B | There is at least one member of category A that is not a member of category B. | Some students are not athletes. |
Additional Information on Syllogism and Logic
Syllogism problems test your ability to reason based *only* on the information provided in the statements, even if the statements contradict common knowledge. The key is to follow the logical structure.
Statements involving "Some" establish the existence of an overlap. They are symmetrical, meaning "Some A are B" is the same as "Some B are A". However, they do not support conclusions about "All" members of a category. To conclude "All A are B", you typically need statements that establish that the entire category A is included within category B.
Visualizing with diagrams (like Venn diagrams) can be helpful, but the formal rules of inference are the most reliable way to solve these problems accurately. Remember to only accept conclusions that are *necessarily* true based on the premises.
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:
No bank is an office.
All offices are stalls.
Conclusions:
I. No bank is a stall.
II. No stall is a bank.
III. Some stalls are offices.
IV. All the stalls are offices
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 flowers are beautiful.
Vaidehi is beautiful.
Conclusions:
I. Vaidehi is a flower.
II. Some beautiful are flowers.
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 rugs are blankets.
2. All blankets are pillows.
3. Some blankets are frames.
Conclusions:
I. All pillows are rugs.
II. Some pillows are rugs.
III. All rugs are frames
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 fingers are toes.
Some toes are rings.
Some rings are hands.
Conclusions:
I. Some hands are toes.
II. Some rings are fingers.
III. Some hands are fingers.
V. Some fingers are rings.
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 polygons are angles.
All angles are diagonals.
All cones are cubes.
All cubes are decagons.
No diagonal is a cube.
Conclusions:
I. Some diagonals are polygons.
II. All diagonals are decagons.
III. No polygon is a cone.
IV. Some cubes are angles.
