I need help setting up this problem: Write the set of points from -7 to 1 but excluding -4 and 1 as a union of intervals.
To set up the problem of writing the set of points from -7 to 1 but excluding -4 and 1 as a union of intervals, you'll need to break down the given interval into smaller intervals, including the endpoints, and then exclude the intervals that contain -4 and 1.
Here's how you can do it step by step:
1. Start with the given interval [-7, 1].
2. Begin by finding intervals that include -7 and -4. Since -7 is the starting point, we include it in the first interval. However, since -4 needs to be excluded, create a new interval right after it.
3. The first interval is [-7, -4). Square brackets indicate that the endpoint is included, while the parenthesis means the endpoint is excluded.
4. Proceed to find intervals that exclude both -4 and 1. Since -4 needs to be excluded, create a new interval right after it. Similarly, since 1 needs to be excluded, create a new interval before it.
5. The second interval is (-4, 1). Both endpoints are excluded as indicated by the parentheses.
6. Finally, combine the two intervals to form the union. The set of points from -7 to 1, excluding -4 and 1, as a union of intervals can be represented as follows: [-7,-4) ∪ (-4,1).
Remember, in set notation, the symbol "∪" denotes the union of two sets.