Given below are three statements and four conclusions drawn based on the statements. Conclusion I: Some writers are engineers.
Statement 1: Some engineers are writers.
Statement 2: No writer is an actor.
Statement 3: All actors are engineers.
Conclusion II: All engineers are actors.
Conclusion III: No actor is a writer.
Conclusion IV: Some actors are writers.
Which one of the following options can be logically inferred?
Logical Inference Solution
This solution analyzes the given statements and conclusions to identify the logically valid inferences required for exam success.
Analyzing the Statements
We are given three premises:
- Statement 1: Some engineers are writers.
- Statement 2: No writer is an actor.
- Statement 3: All actors are engineers.
Evaluating the Conclusions
Let's assess each conclusion based on the statements:
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Conclusion I: Some writers are engineers.
This is correct. Statement 1 ("Some engineers are writers") is a symmetrical relationship. If at least one engineer is a writer, then at least one writer must be an engineer.
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Conclusion II: All engineers are actors.
This is incorrect. Statement 3 ("All actors are engineers") means the group 'actors' is a subset of 'engineers'. It does not imply the reverse. Furthermore, Statements 1 and 2 combined show that engineers who are writers cannot be actors, disproving that *all* engineers are actors.
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Conclusion III: No actor is a writer.
This is correct. Statement 2 ("No writer is an actor") is logically equivalent to "No actor is a writer." The relationship is mutual exclusion.
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Conclusion IV: Some actors are writers.
This is incorrect. Statement 2 ("No writer is an actor") directly contradicts this conclusion. If no writer is an actor, then no actor can be a writer.
Determining the Correct Option
Conclusions I and III are logically derived from the provided statements.
The option that correctly identifies these conclusions is the one stating "Only conclusion I and conclusion III are correct."
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?
