Write the set of points from −5 to 1 but excluding 0 and 1 as a union of intervals:
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To write the set of points from -5 to 1 but excluding 0 and 1 as a union of intervals, we can break it down into three intervals.
1) (-5, 0): This represents all the numbers between -5 and 0, excluding 0 itself.
2) (0, 1): This represents all the numbers between 0 and 1, excluding both 0 and 1.
3) (1, 1): This is an empty set since the interval (1, 1) does not contain any numbers.
Therefore, the set of points from -5 to 1 but excluding 0 and 1 can be written as the union of intervals (-5, 0) and (0, 1), denoted as:
(-5, 0) ∪ (0, 1)
To write the set of points from −5 to 1 (excluding 0 and 1) as a union of intervals, we can break it down into smaller intervals. We will express the intervals from −5 to 1 using mathematical notation with square brackets for closed intervals and parentheses for open intervals:
1. The interval from -5 to 0 (excluding 0): (-5, 0)
2. The interval from 0 to 1 (excluding 0 and 1): (0, 1)
Therefore, the set of points from −5 to 1 (excluding 0 and 1) can be written as the union of these intervals: (-5, 0) ∪ (0, 1).