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Consider the following statements to be ...

Consider the following statements to be true even if they seem to be at variance from commonly known facts and decide which of the conclusions logically follows from the statements.
Statement:
• Some spoons are glasses.
• All the plates are glasses.
Conclusions:
1. Some glasses are plates.
2. Some glasses are spoons,

A

Only conclusion 1 follows

B

Neither conclusion 1 nor 2 follows

C

Both conclusions 1 and 2 follow

D

Only conclusion 2 follows

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the given statements and conclusions logically. Let's break it down step by step. ### Step 1: Understand the Statements 1. **Statement 1**: Some spoons are glasses. 2. **Statement 2**: All the plates are glasses. ### Step 2: Visualize with Venn Diagrams To better understand the relationships, we can use Venn diagrams: - Draw a circle for **Spoons** (S). - Draw a circle for **Glasses** (G). - Shade the area where some spoons overlap with glasses to represent "Some spoons are glasses". Next, draw another circle for **Plates** (P) that is entirely within the **Glasses** circle, since "All plates are glasses". ### Step 3: Analyze the Conclusions Now, we will evaluate the conclusions based on the Venn diagram. #### Conclusion 1: Some glasses are plates. - Since all plates are within the glasses circle, it logically follows that some part of the glasses must be plates. Therefore, this conclusion is **true**. #### Conclusion 2: Some glasses are spoons. - The statement "Some spoons are glasses" indicates that there is an overlap between the spoons and glasses circles. However, we cannot definitively conclude that "some glasses are spoons" because the overlap does not guarantee that all parts of glasses contain spoons. Thus, this conclusion is **not necessarily true**. ### Step 4: Final Decision Based on the analysis: - Conclusion 1 is true. - Conclusion 2 is not necessarily true. ### Final Answer Only Conclusion 1 follows from the statements. ---
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