Two statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All roads are routes.
All routes are bridges.
Conclusions:
I.Some routes are roads.
II.All roads are bridges.
Correct Answer :
Both conclusions I and II follow
Solution :
The correct answer is Both conclusions I and II follow.
Step-by-step Explanation:
1. Analyze the given statements:
Statement 1: "All roads are routes." (This means the set of all roads is entirely contained within the set of routes.)
Statement 2: "All routes are bridges." (This means the set of all routes is entirely contained within the set of bridges.)
2. Evaluate Conclusion I ("Some routes are roads"):
From Statement 1, we know that all roads are routes. In deductive logic, if all elements of category A are contained within category B, it implies that at least some elements of category B are contained in category A. Therefore, "Some routes are roads" logically follows as a valid conversion of Statement 1.
3. Evaluate Conclusion II ("All roads are bridges"):
Combining Statement 1 ("All roads are routes") and Statement 2 ("All routes are bridges") transitively proves that the set of roads is completely contained within the set of bridges. Therefore, "All roads are bridges" logically follows.
Since both conclusion I and conclusion II logically follow from the given statements, the correct option is Both conclusions I and II follow.
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