In each question below, some statements are given followed by some conclusions. You have to assume everything in the statements to be true even if they seem to be at variance with commonly known facts. Now, decide which of the two given conclusions logically follow from the statements, disregarding commonly known facts.
Statements:
All manager are help.
Only a few help are free.
Some free is not rude.
Conclusions:
I. All help being rude is a possibility.
II. Some manager is help.
Correct Answer :
Both I and II follow
Solution :
The correct option is: Both I and II follow.
Let us analyze the statements and test the logical validity of the conclusions one by one.
1. Analyzing Statement Details:
- "All manager are help": This means the entire set of "manager" is contained inside the set of "help" ().
- "Only a few help are free": This has two parts: "Some help are free" and "Some help are not free".
- "Some free is not rude": There is at least some part of the set "free" that does not overlap with the set "rude".
2. Evaluating Conclusion I: "All help being rude is a possibility"
- We are given that "Some free is not rude". This restricts a portion of the "free" set from being "rude".
- However, there is no direct negative relationship or restriction preventing the set of "help" from being completely inside "rude".
- We can construct a possible Venn diagram where the entire set of "help" (along with "manager", since "All manager are help") is placed inside "rude", while still satisfying "Some free is not rude" by keeping that non-overlapping portion of "free" outside "rude".
- Since such a configuration is possible without violating any of the given statements, Conclusion I is a valid possibility. Thus, Conclusion I follows.
3. Evaluating Conclusion II: "Some manager is help"
- We are given the statement "All manager are help".
- By definition, if all members of the set "manager" belong to the set "help", then (assuming the set of managers is non-empty) there must be some managers who are help. In syllogism rules, "All" logically implies "Some".
- Therefore, Conclusion II definitely and directly follows from the first statement.
Since both Conclusion I and Conclusion II logically follow from the given statements, the correct option is "Both I and II follow".
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