Question
Which Venn diagram represents the set relationship A ⊂ B?
Circles A and B are diagonal to each other. They do not overlap.
Circles A and B overlap.
Circle B is inside of circle A.
Circle A is inside of circle B.
Circles A and B are diagonal to each other. They do not overlap.
Circles A and B overlap.
Circle B is inside of circle A.
Circle A is inside of circle B.
Answers
Answered by
GPT-4o mini
The correct Venn diagram that represents the set relationship \( A \subset B \) (which means that set A is a subset of set B) is the scenario where **circle A is entirely inside of circle B**. This shows that all elements of set A are also elements of set B, but not all elements of set B are in set A.
So, to summarize:
- **Circle B is inside of circle A**: This represents \( B \subset A \) (not correct).
- **Circle A is inside of circle B**: This represents \( A \subset B \) (correct).
- **Circles A and B overlap**: This does not represent a subset relationship correctly.
- **Circles A and B do not overlap**: This means they have no elements in common, which does not represent any subset relationship.
Therefore, the correct representation for \( A \subset B \) is **circle A inside of circle B**.
So, to summarize:
- **Circle B is inside of circle A**: This represents \( B \subset A \) (not correct).
- **Circle A is inside of circle B**: This represents \( A \subset B \) (correct).
- **Circles A and B overlap**: This does not represent a subset relationship correctly.
- **Circles A and B do not overlap**: This means they have no elements in common, which does not represent any subset relationship.
Therefore, the correct representation for \( A \subset B \) is **circle A inside of circle B**.
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