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Consider the given statements to be true...

Consider the given statements to be true even if they seem to be at variance with the commonly known facts and decide which of the given conclusions logically follows (s) from the statements.
Statements :
Some metals are iron.
Some iron are heavy.
Conclusion :
1. All iron are metals.
2. All heavy are metals.

A

Only conclusion 2 follows

B

No conclusion follows

C

All the conclusions follows

D

Only conclusion 1 follows

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we will analyze the given statements and conclusions step by step. ### Step 1: Understand the Statements We have two statements: 1. Some metals are iron. 2. Some iron are heavy. ### Step 2: Visualize with Venn Diagrams To better understand the relationships, we can use a Venn diagram: - Let one circle represent "Metals." - Let another circle represent "Iron." - Let a third circle represent "Heavy." From the first statement, "Some metals are iron," we can draw an overlap between the "Metals" circle and the "Iron" circle. From the second statement, "Some iron are heavy," we can draw an overlap between the "Iron" circle and the "Heavy" circle. ### Step 3: Analyze the Conclusions Now we will analyze the conclusions based on the information from the statements. **Conclusion 1: All iron are metals.** - This conclusion states that every iron is a metal. However, the statements only indicate that some metals are iron, not all. Therefore, this conclusion does not logically follow from the statements. **Conclusion 2: All heavy are metals.** - This conclusion states that every heavy object is a metal. The statements do not provide any information that supports this conclusion. We only know that some iron are heavy, but we cannot conclude that all heavy items are metals. Therefore, this conclusion also does not logically follow from the statements. ### Step 4: Final Decision Since neither conclusion logically follows from the statements, we conclude that: - **No conclusion follows.** ### Summary of the Solution - Conclusion 1 is incorrect because the statements do not support the idea that all iron are metals. - Conclusion 2 is incorrect because there is no information to suggest that all heavy items are metals. - Therefore, the answer is that no conclusion follows.
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