Understanding the Logical Reasoning Problem
This question asks us to determine which conclusions logically follow from two given statements. We need to assume the statements are true, even if they seem unusual in the real world, and apply logical deduction.
Analyzing the Statements
Let's break down the information provided:
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Statement 1: All chips are biscuits.
This means that the category 'chips' is entirely contained within the larger category 'biscuits'. If something is a chip, it must also be a biscuit. Using set notation, if C represents the set of Chips and B represents the set of Biscuits, then $C \subseteq B$.
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Statement 2: No wafer is a chip.
This means that the categories 'wafer' and 'chip' are completely separate. Nothing can be both a wafer and a chip. Using set notation, if W represents the set of Wafers, then the intersection of W and C is empty: $W \cap C = \emptyset$.
Evaluating the Conclusions
Now, let's examine each conclusion based on these statements:
Conclusion I: Some biscuits are wafers.
From Statement 1, we know that chips are a part of biscuits ($C \subseteq B$). Statement 2 tells us that wafers are separate from chips ($W \cap C = \emptyset$). Does this mean wafers must overlap with biscuits? Not necessarily. It's possible that wafers are a type of biscuit that isn't a chip. In this case, 'Some biscuits are wafers' would be true. For example, imagine Biscuits = {Chip1, Chip2, WaferBiscuit}, Chips = {Chip1, Chip2}, Wafers = {WaferBiscuit}. This satisfies both statements, and Conclusion I is true.
Conclusion II: No wafer is a biscuit.
This conclusion states that the sets 'wafer' and 'biscuit' are completely separate ($W \cap B = \emptyset$). Is this guaranteed by the statements? Consider a scenario where wafers are completely different from biscuits. For example, Biscuits = {Chip1, Chip2}, Chips = {Chip1, Chip2}, Wafers = {Wafer1, Wafer2} (where Wafer1 and Wafer2 are neither chips nor biscuits). This also satisfies both statements ('All chips are biscuits' and 'No wafer is a chip'), and in this case, Conclusion II ('No wafer is a biscuit') would be true.
Conclusion III: Some chips are wafers.
Statement 2 clearly states, "No wafer is a chip." This directly contradicts Conclusion III, "Some chips are wafers." Therefore, Conclusion III cannot logically follow from the given statements. Using set notation, $W \cap C = \emptyset$, which means there cannot be any element 'x' such that $Chip(x)$ and $Wafer(x)$ are both true.
Determining Which Conclusions Logically Follow
We have established that Conclusion III is definitely false.
Conclusions I and II are contradictory. If 'Some biscuits are wafers' is true, then 'No wafer is a biscuit' must be false. Conversely, if 'No wafer is a biscuit' is true, then 'Some biscuits are wafers' must be false.
The premises ($C \subseteq B$ and $W \cap C = \emptyset$) do not force a specific relationship between Wafers (W) and Biscuits (B). The premises allow for scenarios where W and B overlap (making Conclusion I true), and they also allow for scenarios where W and B are completely separate (making Conclusion II true).
Since the two statements do not provide enough information to decide whether Wafers overlap with Biscuits or not, we cannot definitively say that Conclusion I *must* be true, nor can we say that Conclusion II *must* be true.
However, in logical reasoning tests structured like this, when two conclusions are contradictory, and the premises allow for possibilities supporting each conclusion, the correct logical outcome is often expressed as "Either conclusion I or II follows". This signifies that the actual state of affairs must be one of the two possibilities allowed by the premises.
Therefore, the logically correct choice is that either Conclusion I or Conclusion II must follow from the statements.
Final Answer
Based on the analysis, the correct option is the one stating that either Conclusion I or II follows.
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 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 C are P.
No C is a T.
All P are S.
Conclusions :
I. All S being C is a possibility.
II. At least some T are not C.
III. Some P are not T's.
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:
All cups are saucers.
No saucer is a plate.
Conclusions:
I. Some cups are plates.
II. No cup is a plate.
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 cubs are trucks.
All trucks are lanterns.
No lanterns are bricks.
Conclusions:
I. Some cubs are lanterns.
II. Some trucks are not bricks.
III. All cubs are trucks.
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 locks are keys.
Some keys are passwords.
Conclusions:
I. Some passwords are locks.
II. All passwords are locks.
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.
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.
