In each of the questions below some statements are given followed by two conclusions. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements:
Some report is launch.
All launch is year.
No year is leave.
Conclusion:
I. No launch is leave
II. Some report is not leave is a possibility.
Correct Answer :
If only conclusion I follows.
Solution :
The correct option is: If only conclusion I follows.
Let us analyze the logical connections between the given statements step-by-step using standard syllogism rules and Venn diagram concepts.
Given Statements:
1. Some report is launch.
2. All launch is year.
3. No year is leave.
Step-by-Step Analysis of Conclusions:
Conclusion I: No launch is leave
From Statement 2, we know that all elements of "launch" reside entirely within "year". From Statement 3, we know that no element of "year" can be part of "leave" (they are completely disjoint sets).
Since all "launch" is inside "year", and no "year" can touch "leave", it logically follows that no "launch" can touch "leave". Therefore, "No launch is leave" is a definite true conclusion.
Conclusion II: Some report is not leave is a possibility.
Let us evaluate the definite relationship between "report" and "leave":
- From Statement 1, "Some report is launch".
- Since all "launch" is "year", those specific "reports" that are "launch" are also "year".
- Since no "year" is "leave", those specific "reports" that are "year/launch" can NEVER be "leave".
Thus, it is already a definite fact that "Some report is not leave" (specifically, the part of report that overlaps with launch/year).
In logic, when a statement is already a definite fact, expressing it as a "possibility" makes the conclusion invalid/false in absolute terms (a certainty is not merely a possibility).
Therefore, only Conclusion I logically follows from the given statements.
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