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 chess is a can.
Not a single can is a horn.
Every horn is an adapter.
Conclusions:
I. Some adapters which are horns are chess as well.
II. No chess is a horn.
III. Some adapters are horns.
Understanding the Statements
We are given three statements and three conclusions. Our task is to determine which conclusions logically follow from the statements, assuming the statements are true, even if they contradict common knowledge.
- Statement 1: No chess is a can. (This means the categories 'chess' and 'can' are entirely separate; they have no members in common. Mathematically, Chess ∩ Can = ∅).
- Statement 2: Not a single can is a horn. (This means the categories 'can' and 'horn' are entirely separate. Mathematically, Can ∩ Horn = ∅).
- Statement 3: Every horn is an adapter. (This means the entire category of 'horn' is included within the category of 'adapter'. Mathematically, Horn ⊆ Adapter).
Analyzing the Conclusions
Now, let's examine each conclusion to see if it can be logically derived from the statements.
Conclusion I: Some adapters which are horns are chess as well.
This conclusion suggests that there is an overlap between the group of 'adapters that are horns' and the group of 'chess'. Since Statement 3 tells us that every horn is an adapter, the phrase 'adapters which are horns' simply refers to 'horns'. So, the conclusion is essentially asking if some horns are also chess (Horn ∩ Chess ≠ ∅).
Let's review the statements:
- Chess and Cans are separate.
- Cans and Horns are separate.
- All Horns are Adapters.
The statements establish that chess is separate from cans, and horns are separate from cans. They also state that horns are a type of adapter. However, there is no information given that links chess directly or indirectly (through other categories like 'can' or 'adapter') to horns. It's possible that the set of chess and the set of horns are completely distinct. Because the statements do not force an overlap between chess and horns, this conclusion does not necessarily follow.
Conclusion II: No chess is a horn.
This conclusion claims that the categories 'chess' and 'horn' are mutually exclusive (Chess ∩ Horn = ∅).
Similar to the analysis for Conclusion I, the given statements do not provide enough information to definitively conclude that no chess can be a horn. The 'can' category separates chess from horns, but this separation doesn't prevent chess and horns from overlapping. We can imagine a scenario where these statements are true, but a chess piece could also be classified as a horn:
- Let Chess = {Item A, Item C}
- Let Can = {Item B}
- Let Horn = {Item C}
- Let Adapter = {Item C, Item D}
Checking the statements with this scenario:
- Statement 1: No chess is a can ({Item A, Item C} ∩ {Item B} = ∅) - True.
- Statement 2: No can is a horn ({Item B} ∩ {Item C} = ∅) - True.
- Statement 3: Every horn is an adapter ({Item C} ⊆ {Item C, Item D}) - True.
Now check Conclusion II:
- Conclusion II: No chess is a horn ({Item A, Item C} ∩ {Item C} = {Item C}). Since the intersection is not empty ({Item C}), this conclusion is False in this specific valid scenario.
Because we found a situation where the statements are true but the conclusion is false, Conclusion II does not logically follow.
Conclusion III: Some adapters are horns.
This conclusion states that there exist items that belong to both the 'adapter' category and the 'horn' category (Adapter ∩ Horn ≠ ∅).
Statement 3 says, "Every horn is an adapter" (Horn ⊆ Adapter).
This statement directly implies that if something is a horn, it must also be an adapter. Assuming that the category 'horn' is not empty (i.e., there exists at least one horn), then that horn is automatically an adapter. Therefore, it logically follows that some adapters are indeed horns.
This conclusion is valid.
Final Verdict
After analyzing each conclusion against the provided statements:
- Conclusion I: Does not logically follow.
- Conclusion II: Does not logically follow.
- Conclusion III: Logically follows.
Therefore, the only conclusion that is guaranteed to be true based on the given statements is Conclusion III.
Similar Questions
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:
No book is a novel.
All novels are diaries.
Conclusions:
I. All diaries can never be books.
II. Some books are diaries.
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 rhombuses are tangents.
All chords are tangents.
Conclusions:
I. Some rhombuses being chords is a possibility.
II. Some tangents are rhombuses.
Three statements are followed by three conclusions numbered I, II, III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follows from the given statements.
Statements :
No Mango is a banana.
No banana is a guava.
Some guavas are oranges.
Conclusions :
(I) Some mangoes are oranges.
(II) Some guavas are mangoes.
(III) No orange is a banana.
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 tigers are fishes.
No elephant is a tiger.
Some deer are tigers.
Conclusions:
I. Some fishes are deer.
II. No elephant is a deer.
III. No deer is a fish.
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.
Statement :
All Bananas are Grapes.
All Papayas are Pineapple.
Some Pineapples are Banana.
Conclusions:
(I) Some Papayas are Grapes.
(II) Some Grapes are Pineapples.
(III) Some Bananas are Papayas.
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 defects are problems.
Some problems are solutions.
Conclusions:
I. Some defects being solutions is a possibility.
II. No solution is a defect.
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:
Some bags are sacks.
Some sacks are juts.
Conclusions:
I. Some bags are juts.
II. Some juts are sacks.
Two statements are given, followed by two conclusions numbered I and II. Taking the statements to be true, even if they seem to be at variance from commonly known facts, decide which of the conclusions logically follows from the statements.
Statements:
All cycles are buses.
Some buses are trains.
Conclusions:
I. No cycle is train.
II. All cycles are trains.
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.
Statement:
Some figs are orange.
All oranges are grapes.
All mangoes are oranges.
Conclusions:
(I) Some figs are grapes.
(II) All mangoes are grapes.
(III) Some mangoes are figs.
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.
Statement :
All shoes are slippers.
All slippers are socks.
All socks are sandals
Conclusions:
(I) Some sandals are slippers
(II) Some socks are shoes.
(III) All sandals are shoes.
Important Questions from Syllogism
The statements below are followed by conclusions labeled I, II and III. 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:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.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 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:
All Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled I, II and III. 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 women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
The 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 teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
The 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:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
