Given below are two statements and four conclusions drawn based on the Conclusion I: Some clean objects are soaps. Which one of the following options can be logically inferred?
statements.
Statement 1: Some soaps are clean.
Statement 2: All clean objects are wet.
Conclusion II: No clean object is a soap.
Conclusion III: Some wet objects are soaps.
Conclusion IV: All wet objects are soaps.
Logical Reasoning: Statements and Conclusions
This problem involves analyzing two statements to determine which of the given conclusions can be logically inferred.
Analyzing the Statements
- Statement 1: Some soaps are clean. (This means there's an overlap between the set of soaps and the set of clean things).
- Statement 2: All clean objects are wet. (This means the entire set of clean things is contained within the set of wet things).
Evaluating the Conclusions
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Conclusion I: Some clean objects are soaps.
If "Some soaps are clean", then it must be true that "Some clean objects are soaps". This is a valid conversion of the first statement. Therefore, Conclusion I is correct.
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Conclusion II: No clean object is a soap.
This conclusion directly contradicts Statement 1 ("Some soaps are clean"). Therefore, Conclusion II is incorrect.
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Conclusion III: Some wet objects are soaps.
From Statement 1, we know some soaps are clean. From Statement 2, we know all clean things are wet. Combining these, the soaps that are clean must also be wet. This implies that some soaps are wet, and therefore, some wet objects are soaps. Conclusion III is correct.
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Conclusion IV: All wet objects are soaps.
Statement 2 tells us "All clean objects are wet", but not the reverse. We cannot conclude that all wet objects are soaps based on the given information. Therefore, Conclusion IV is incorrect.
Final Deduction
Based on the step-by-step analysis, only Conclusion I and Conclusion III logically follow from the given statements.
Important Questions from Syllogism
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.- Given below are four statements.
Statement 1: All students are inquisitive.
Statement 2: Some students are inquisitive.
Statement 3: No student is inquisitive.
Statement 4: Some students are not inquisitive.
From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class. - Based only on the truth of the statement ‘Some humans are intelligent', which one of the following options can be logically inferred with certainty?
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?
