If A = {S} , which of the following is a correct statement ?

Options

A. `S in A `
B. `S sub A `
C. `{S} in A `
D. `A = S `

Answer

To solve the problem, we need to analyze the set A and the options given.

1. **Understanding the Set A**:
- We are given that \( A = \{ S \} \). This means A is a set that contains one element, which is the set S itself.

2. **Analyzing the Options**:
- **Option 1**: \( S \in A \)
- This statement means that S is an element of the set A. Since A contains S, this statement is true.
- **Option 2**: \( S \subseteq A \)
- This statement means that every element of S is also an element of A. However, since A contains only the set S and not the elements of S, this statement is false.
- **Option 3**: \( S \text{ is a set that belongs to } A \)
- This statement is similar to Option 1. It suggests that S is an element of A. Since A contains S, this statement is also true.
- **Option 4**: \( A = S \)
- This statement suggests that A is equal to S. However, A is a set containing S, not equal to S itself. Therefore, this statement is false.

3. **Conclusion**:
- The correct statements are:
- Option 1: \( S \in A \) is true.
- Option 3: \( S \text{ is a set that belongs to } A \) is also true.
- However, since the question asks for the correct statement and typically only one option is expected to be correct, we conclude that the best answer is Option 1: \( S \in A \).

**Final Answer**: The correct statement is \( S \in A \).

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