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Statements: 1. All roads are waters 2....

Statements: 1. All roads are waters
2. Some waters are boats
Conclusions: 1. Some boats are roads
2. All waters are boats

A

only conclusion 1 follows,

B

only conclusion 2 follows,

C

either conclusion 1 or 2 follows,

D

neither conclusion 1 nor 2 follows,

Text Solution

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The correct Answer is:
To solve the problem, we need to analyze the given statements and conclusions logically. ### Step-by-Step Solution: 1. **Understanding the Statements**: - **Statement 1**: "All roads are waters." - This means that every road is included in the category of waters. - We can represent this with a Venn diagram where the circle representing roads is completely inside the circle representing waters. - **Statement 2**: "Some waters are boats." - This indicates that there is at least a part of the waters that overlaps with the boats. - In the Venn diagram, the circle representing boats will overlap with the circle representing waters. 2. **Drawing the Venn Diagram**: - Draw a large circle for waters. - Inside this circle, draw a smaller circle for roads (since all roads are waters). - Draw another circle for boats that overlaps with the waters circle. 3. **Analyzing the Conclusions**: - **Conclusion 1**: "Some boats are roads." - To check this, we look at the Venn diagram. The circle for roads is entirely within the waters circle, and there is no indication that it overlaps with the boats circle. - Therefore, we cannot conclude that "some boats are roads." This conclusion is **false**. - **Conclusion 2**: "All waters are boats." - This conclusion suggests that the entire waters circle is contained within the boats circle. However, our Venn diagram shows that only some part of the waters overlaps with the boats. - Thus, we cannot conclude that "all waters are boats." This conclusion is also **false**. 4. **Final Decision**: - Since both conclusions are false, we conclude that neither conclusion follows from the statements. ### Answer: The correct option is: **Neither conclusion 1 nor 2 follows.** ---
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MCGROW HILL PUBLICATION-ADDITIONAL TOPICS IN MENTAL MATH-EXERCISE 2
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