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The problem is asking to determine the set \( A = \{x \in \mathbb{R} \mid x > 3 \iff x \geq 6\} \).

### Key Points:
- The symbol "↔" (if and only if) implies that the condition \( x > 3 \) must hold exactly when \( x \geq 6 \).
- This condition suggests that the set includes numbers where \( x \geq 6 \), but excludes values between \( 3 \) and \( 6 \), as those don't satisfy both conditions simultaneously.

### Interpretation:
For \( x \in A \), the only values that satisfy both conditions are:
- \( x \geq 6 \), since for these numbers, both \( x > 3 \) and \( x \geq 6 \) are true.
- Therefore, the solution excludes the interval between \( 3 \) and \( 6 \), which means \( x > 3 \) is only valid when \( x \geq 6 \).

### Solution:
The correct set representing \( A \) is \( (6, \infty) \).

Thus, the correct answer is **B) \( (6, \infty) \)**.

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Would you like further details or have any questions? Here are some related questions:

1. What is the difference between "if" and "if and only if" in logical statements?
2. How would the solution change if the condition were just \( x > 3 \)?
3. Can you graph the intervals involved in this solution?
4. How does interval notation work when dealing with open and closed intervals?
5. What happens to the solution if the condition is \( x \geq 3 \)?

**Tip**: When analyzing logical conditions like "if and only if," it's useful to break down the statement into its individual conditions and check for overlap in values.

Determine the set A = {x ∈ ℝ | x > 3 ↔ x ≥ 6}

In this problem, we determine the set A where x belongs to real numbers with the condition x > 3 if and only if x ≥ 6. This problem uses set theory and logical equivalence to analyze the intervals and set differences. Suitable for students in Grades 10-12.

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