Question

Зображіть проміжки на координатній та запишіть іх періз та об’єднання : 1) (−3;1) i (0;4]; 2) [3;8) i [4;5); 3) (-∞; 3) i (2,8; 4). ДАМ 50 БАЛЛОВ СРОЧНО

Answer 1

Ответ:

1) Проміжок (-3;1) є відкритим зліва, а проміжок (0;4] є закритим зправа. Об'єднання цих проміжків: (-3;1) ∪ [0;4].

2) Проміжок [3;8) є закритим зліва, а проміжок [4;5) є відкритим зправа. Об'єднання цих проміжків: [3;5).

3) Проміжок (-∞;3) є відкритим зліва, а проміжок (2,8;4) є відкритим з обох боків. Об'єднання цих проміжків: (-∞;3) ∪ (2,8;4).

Answer 2

Prominences on the Coordinate Plane

To determine the intervals and their unions and intersections on the given coordinate plane, we need to analyze the given intervals:

1. (−3,1): This interval represents all real numbers between -3 and 1, excluding the endpoints. In interval notation, it can be written as (-3, 1).

2. (0,4]: This interval represents all real numbers between 0 and 4, including the endpoint 4. In interval notation, it can be written as [0, 4].

3. [3,8): This interval represents all real numbers between 3 and 8, excluding the endpoint 8. In interval notation, it can be written as [3, 8).

4. [4,5): This interval represents all real numbers between 4 and 5, excluding the endpoint 5. In interval notation, it can be written as [4, 5).

5. (-∞, 3): This interval represents all real numbers less than 3. In interval notation, it can be written as (-∞, 3).

6. (2,8; 4): This interval represents all real numbers between 2 and 8, excluding the endpoints 2 and 8, and also excluding 4. In interval notation, it can be written as (2, 8) \ {4}.

Union and Intersection of the Intervals

To find the union and intersection of the given intervals, we can analyze the intervals and determine the overlapping regions:

- The union of intervals is the combination of all the numbers that belong to any of the given intervals. It includes all the numbers that are present in at least one of the intervals.

- The intersection of intervals is the set of numbers that are common to all the given intervals. It includes only the numbers that are present in all the intervals.

Now, let's determine the union and intersection of the given intervals:

- The union of the intervals is (-∞, 1) ∪ [0, 8). This means it includes all real numbers less than 1, and all real numbers between 0 and 8, excluding the endpoint 8.

- The intersection of the intervals is [4, 5). This means it includes only the numbers that are common to all the given intervals, which is the interval between 4 and 5, excluding the endpoint 5.

Therefore, the union of the given intervals is (-∞, 1) ∪ [0, 8), and the intersection is [4, 5).

I hope this explanation helps! If you have any further questions, feel free to ask.