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.
Similar Questions
Read the following statement carefully and identify the conclusion that follows.
Statement:
All games are entertainment.
All entertainment is fun.
Conclusions:
I. All games are fun
II. Some fun is entertainment.
Read the following statement carefully and identify the conclusion that follows.
Statement:
All engineers are skilled. No unskilled person is allowed.
Conclusions:
I. All engineers are allowed.
II. No skilled person is unskilled.
Read the following statement carefully and identify the conclusion that follows.
Statement:
All boxes are bags. Some bags are blue. No blue is a plastic.
Conclusions:
I. Some boxes are not plastic.
II. All plastics are bags.
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 coolers are mixers.
Some mixers are scissors.
Some scissors are knives.
Conclusions:
I. Some knives are mixers.
II. Some scissors are coolers.
III. Some knives are coolers.
IV. No knife is a mixer.
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 rice are grains.
All pulses are grains.
All grains are edibles.
Conclusions:
I. All rice are edibles.
II. All pulses are edible.
III. Some edibles are grains.
In this question, 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 follows/follow from the statements.
Statements:
All balls are flowers.
All flowers are plates.
Some plates are cups.
Conclusions:
I. Some flowers are balls.
II. Some plates are flowers.
III. All cups are plates.
Three statements are given followed by three conclusions numbered I, II and Ill. Question ID: 264330143712 Status : Answered Chosen Option : 1 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 males are boys.
Some teachers are boys.
All students are teachers.
Conclusions:
I. Some boys are males.
II. Some teachers are students.
Ill. All males are students.
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 curtains are doormats.
Some doormats are pillows.
Some pillows are bedsheets.
Conclusions:
I. Some bedsheets are doormats.
II. Some bedsheets are curtains.
III. Some pillows are doormats.
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 sweets are chocolates.
All chocolates are cookies.
Some cookies are healthy.
Conclusions:
I. Some sweets are cookies.
II. Some cookies are chocolates.
III. Some chocolates are sweets.
In this question, 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 conclusion(s) logically follows/follow from the statements.
Statements:
All cricketers are wealthy.
Some wealthy are Indians.
All Indians are honest.
Conclusions:
I. All Indians are cricketers.
II. Some cricketers are honest.
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.
