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Read the following statements and the co...

Read the following statements and the conclusions that follow. Decide which of the two conclusions follow from the given statements.
Statements:
* All the cots are hotels.
* All hotels are sheets.
Conclusions:
1. Some cots are not sheets.
2. Some sheets are cots.
(a)Both conclusions 1 and 2 follow
(b)Only conclusion 2 follows
(c)Either conclusion 1 or 2 follows
(d)Only conclusion 1 follows

A

Both conclusions 1 and 2 follow

B

Only conclusion 2 follows

C

Either conclusion 1 or 2 follows

D

Only conclusion 1 follows

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we will analyze the statements and conclusions step by step. ### Step 1: Understand the Statements We have two statements: 1. All the cots are hotels. 2. All hotels are sheets. From these statements, we can infer the following relationships: - Since all cots are hotels, every cot is included in the category of hotels. - Since all hotels are sheets, every hotel (and thus every cot) is also included in the category of sheets. ### Step 2: Create a Venn Diagram To visualize the relationships: - Draw a circle for "Cots" inside a larger circle for "Hotels." - Draw another larger circle for "Sheets" that encompasses the "Hotels" circle. This means: - The "Cots" circle is completely inside the "Hotels" circle. - The "Hotels" circle is completely inside the "Sheets" circle. ### Step 3: Analyze the Conclusions Now, let's evaluate the conclusions based on our Venn diagram. **Conclusion 1:** Some cots are not sheets. - This conclusion states that there are some cots that do not belong to the category of sheets. However, since all cots are hotels and all hotels are sheets, it follows that all cots must also be sheets. Therefore, this conclusion is **false**. **Conclusion 2:** Some sheets are cots. - This conclusion states that there are some sheets that are also cots. Since all cots are included in the category of sheets (as established in our Venn diagram), this conclusion is **true**. ### Step 4: Determine Which Conclusions Follow Based on our analysis: - Conclusion 1 is false. - Conclusion 2 is true. ### Final Answer Only conclusion 2 follows. Therefore, the correct option is: (b) Only conclusion 2 follows. ---
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