Given below are two statements and four conclusions drawn based on the statements. Statement 1: Some bottles are cups. Statement 2: All cups are knives. Conclusion I: Some bottles are knives. Conclusion II: Some knives are cups. Conclusion III: All cups are bottles. Conclusion IV: All knives are cups. Which one of the following options can be logically inferred?
Only conclusion I and conclusion II are correct
Understanding the Syllogistic Statements
The problem presents two statements and four conclusions based on them. We need to determine which conclusions logically follow from the given statements.
Let's denote:
- B = Bottles
- C = Cups
- K = Knives
Statement 1: Some bottles are cups. This can be represented as: Some B are C.
Statement 2: All cups are knives. This can be represented as: All C are K.
Analyzing the Conclusions
We will now analyze each conclusion based on the two statements:
Conclusion I: Some bottles are knives. (Some B are K)
We know that 'Some B are C' (Statement 1) and 'All C are K' (Statement 2). Statement 1 tells us there is at least one bottle that is also a cup. Statement 2 tells us that every cup is also a knife. Therefore, the bottle(s) that are cups must also be knives. This means 'Some B are K' is a valid inference.
Conclusion II: Some knives are cups. (Some K are C)
Statement 2 states 'All C are K'. This means the set of all cups (C) is entirely contained within the set of knives (K). If all cups are knives, then it logically follows that some knives are cups (specifically, those knives that are also cups). This is a valid inference, known as conversion in syllogistic logic for affirmative statements.
Conclusion III: All cups are bottles. (All C are B)
Statement 1 says 'Some B are C'. This only indicates an overlap between the set of bottles and the set of cups. It does not provide information about *all* cups. It is possible that there are cups which are not bottles. Therefore, 'All C are B' cannot be logically inferred from the given statements.
Conclusion IV: All knives are cups. (All K are C)
Statement 2 says 'All C are K'. This means the set of cups is a subset of the set of knives ($C \subseteq K$). This does not imply the reverse relationship, that the set of knives is a subset of the set of cups ($K \subseteq C$). It is possible to have knives that are not cups. Therefore, 'All K are C' cannot be logically inferred.
Final Result
Based on the analysis, Conclusion I and Conclusion II are the only valid inferences from the given statements.
Comparing this with the options provided:
- Option 1: Only conclusion I and conclusion II are correct.
- Option 2: Only conclusion II and conclusion III are correct.
- Option 3: Only conclusion II and conclusion IV are correct.
- Option 4: Only conclusion III and conclusion IV are correct.
The analysis shows that Option 1 is the correct choice.
Important Questions from Reasoning
'Neigh' is related to 'Horse' in the same way as 'Bleat' is related to ____
Three of the following four letter-clusters are alike in a certain way and one is different. Select the odd one.
Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R) :
Assertion (A): Substance is always the subject of all predicates.
Reason (R): Substance is self-existent and self-conceived.
In the light of the above statements. choose the correct answer from the options given below:
Given below is a question followed by three statements. Identify the statements that are necessary to answer the question.
Question: What is the percentage profit gained by a vendor when he sells an article?
Statements:
(i) He gives a 10% discount on the marked price.
(ii) He would have earned 25% profit if he did not give any discount.
(iii) The cost price of the article is Rs. 8000.
Choose the correct option from those given below :
Given below are two statements:
Statement I: Human reason has this peculiar fate that it reaches at a stage when it can neither answer certain questions nor can it ignore such questions.
Statement II: Human reason, by its own nature, is not competent to resolve certain questions concerning the ultimate reality.
In light of the above statements, choose the most appropriate answer from the options given below
