To sketch the set \( X = [1,3] \times [1,2] \), let's break it down:

1. The interval \( [1,3] \) on the x-axis includes all x-values between 1 and 3, including the endpoints.
2. The interval \( [1,2] \) on the y-axis includes all y-values between 1 and 2, including the endpoints.

### Sketching the Set:
- Draw a rectangle on the coordinate plane where:
  - The x-values range from 1 to 3.
  - The y-values range from 1 to 2.
- The corners of this rectangle will be at the points (1, 1), (1, 2), (3, 1), and (3, 2).
- Since the intervals are closed (indicated by the square brackets), the edges of the rectangle are included in the set.

This rectangle represents the Cartesian product \( [1,3] \times [1,2] \), which is the set \( X \).

Would you like any further details or have any questions about this explanation?

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Here are some related questions to consider:

1. What does the Cartesian product represent in general?
2. How would the sketch change if the intervals were open, e.g., \( (1,3) \times (1,2) \)?
3. How do you interpret the Cartesian product when one interval is open and the other is closed?
4. What is the area of the set \( X \) in the plane?
5. How would you describe the boundary of the set \( X \)?

**Tip:** When working with Cartesian products, always consider the type of intervals (open or closed) as they directly affect the boundaries of the set.

Learn how to sketch the set X = [1,3] × [1,2] by understanding Cartesian products and intervals in coordinate geometry. This guide includes a detailed breakdown of the x and y intervals and how to represent them visually as a rectangle on the coordinate plane. Suitable for students in Grades 9-12.

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