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Read the given statement(s) and conclusi...

Read the given statement(s) and conclusions carefully and select which of the conclusions logically follow(s) from the statement(s).
Statement : All gifts are dolls. All dolls are toys.
Conclusions :
1. All gifts are toys.
2. Some toys are gifts

A

Only (2) follows

B

Both (1) & (2) follows

C

Only (1) follows

D

Either (1) or (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**: All gifts are dolls. 2. **Statement 2**: All dolls are toys. ### Step 2: Visualize with Venn Diagrams To better understand the relationships, we can use Venn diagrams: - Draw a circle for "gifts" inside a larger circle for "dolls". - Draw another larger circle that encompasses the "dolls" circle for "toys". This representation shows: - All items in the "gifts" circle are also in the "dolls" circle. - All items in the "dolls" circle are also in the "toys" circle. ### Step 3: Analyze the Conclusions Now let's evaluate the conclusions based on the Venn diagram: 1. **Conclusion 1**: All gifts are toys. - Since all gifts are inside the dolls circle and all dolls are inside the toys circle, it follows that all gifts must also be inside the toys circle. Therefore, this conclusion is **true**. 2. **Conclusion 2**: Some toys are gifts. - Since all gifts are toys (from Conclusion 1), it follows that there are indeed some toys that are gifts. Therefore, this conclusion is also **true**. ### Step 4: Final Decision Both conclusions logically follow from the statements provided. ### Solution Summary: - **Conclusion 1**: True (All gifts are toys). - **Conclusion 2**: True (Some toys are gifts). Thus, both conclusions follow from the statements.
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