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?
Analyzing the Statements
We are given two statements:
- Statement 1: Some bottles are cups.
- Statement 2: All cups are knives.
Evaluating the Conclusions
Conclusion I: Some bottles are knives
Reasoning: Statement 1 establishes an overlap between the set of 'bottles' and 'cups'. Statement 2 states that the entire set of 'cups' is contained within the set of 'knives'. Combining these, the overlap between 'bottles' and 'cups' must also overlap with 'knives'. Therefore, some bottles are indeed knives.
Result: Correct
Conclusion II: Some knives are cups
Reasoning: Statement 2 says 'All cups are knives'. This means the set of 'cups' is a subset of the set of 'knives'. If all cups are knives, then it logically follows that some knives (specifically, those that are also cups) are cups.
Result: Correct
Conclusion III: All cups are bottles
Reasoning: Statement 1 ('Some bottles are cups') only indicates a partial overlap. It does not state that all cups are bottles, nor that all bottles are cups. This conclusion cannot be logically derived.
Result: Incorrect
Conclusion IV: All knives are cups
Reasoning: Statement 2 ('All cups are knives') implies that the set of cups is contained within the set of knives. This does not mean that the set of knives is contained within the set of cups. Therefore, not all knives are necessarily cups.
Result: Incorrect
Final Answer Derivation
Based on the step-by-step analysis:
- Conclusion I is logically inferred.
- Conclusion II is logically inferred.
- Conclusion III is not inferred.
- Conclusion IV is not inferred.
The option that correctly identifies the logically inferred conclusions is the one stating that only Conclusion I and Conclusion II are correct.
Important Questions from Syllogism
- Consider the following sentences:
All benches are beds .No bed is a bulb. Some bulbs are lamps.
Which of the following can be inferred?
i. Some beds are lamps.
ii. Some lamps are beds. Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows.
Statements:
I. No manager is a leader.
II. All leaders are executives.
Conclusions:
I. No manager is an executive.
II. No executive is a manager.Given below are two statements 1 and 2, and two conclusions I and II.
Statement 1: All entrepreneurs are wealthy.
Statement 2: All wealthy are risk seekers.
Conclusion I: All risk seekers are wealthy.
Conclusion II: Only some entrepreneurs are risk seekers.
Based on the above statements and conclusions, which one of the following options is CORRECT?
Statements:
1. All heroes are winners.
2. All winners are lucky people.
Inferences:
I. All lucky people are heroes.
II. Some lucky people are heroes.
III. Some winners are heroes.
Which of the above inferences can be logically deduced from statements 1 and 2?Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?
(i) All human beings are cruel creatures.
(ii) Some human beings are cruel creatures.
(iii) Some creatures that are cruel are human beings.
(iv) No human beings are cruel creatures.
