Question

1) (-бесконечность;10) и (3;6) 2) (-бесконечность; 8]и [7;+бесконечность) 3) [2,4;5) и (4;11] 4) [-1,8;0) и [-1;14] ​

Answer 1

Ответ:

Условие дополнено: "Найдите объединение числовых промежутков"!

1) (-∞; 10) и (-3; 6)  :

(-∞; 10) ∪ (-3; 6)  = (-∞; 10)

2) (-∞; 8] и [7; +∞)  :

(-∞; 8] ∪ [7; +∞) = (-∞; +∞)

3) [2,4; 5) и (4; 11] :

[2,4; 5) ∪ (4; 11] = [2,4; 11]

4) [-1,8; 0) и [-1; 14] :

[-1,8; 0) ∪ [-1; 14] = [-1,8; 14]

Answer 2

To analyze the given intervals, we need to understand interval notation. In interval notation, square brackets "[ ]" indicate that the endpoint is included, while parentheses "( )" indicate that the endpoint is excluded. An infinity symbol is represented as "±∞" (positive infinity or negative infinity). Combining these symbols, we can interpret the intervals as follows:

1. (-∞;10) and (3;6)

This consists of two intervals:

• The first interval is all real numbers less than 10 but excluding 10.
• The second interval is all real numbers between 3 and 6, excluding both 3 and 6.

2. (-∞; 8] and [7;+∞)

This consists of two intervals:

• The first interval is all real numbers less than or equal to 8.
• The second interval is all real numbers greater than or equal to 7.

3. [2.4;5) and (4;11]

This consists of two intervals:

• The first interval is all real numbers between 2.4 and 5, including both 2.4 and 5.
• The second interval is all real numbers between 4 and 11, excluding both 4 and 11.

4. [-1,8;0) and [-1;14]

This consists of two intervals:

• The first interval is all real numbers between -1 and 8, including both -1 and 8.
• The second interval is all real numbers between -1 and 14, including both -1 and 14.

Note: Square brackets indicate that the endpoints are included, and parentheses indicate that the endpoints are excluded.