Question

1. Изобразите на координатной прямой и запишите пересечение и объединение числовых промежутков: [-7; 5) и (бесконечность ; 10].​ ребята помогите пожалуйста умоляю

Answer 1

Пошаговое объяснение:

Множество, составляющее общую часть некоторых множеств А и В, называют пересечением этих множеств и обозначают А∩В. Изобразим на координатной прямой числовые промежутки [-7;5) и

(-∞ ;10] ( рисунок во вложении).

Как видим наши промежутки пересекаются в промежутке [-7 ; 5), значит :

[-7;5) ∩ (-∞ ;10] = [-7 ; 5)

Множество, состоящее из элементов, принадлежащих хотя бы одному из множеств А и В, называют объединением этих множеств обозначают A∪B

По рисунку видно , что числовой промежуток [-7;5) входит в числовой промежуток (-∞ ;10] , значит объединением числовых промежутков будет промежуток  (-∞ ;10], т.е

[-7;5) ∪ (-∞ ;10] = (-∞ ;10]

Answer 2

Representation of Intervals on a Number Line

To represent the intervals [-7; 5) and (infinity; 10] on a number line, we need to understand the notation used for intervals.

- The square bracket [ ] represents that the endpoint is included in the interval. - The round bracket ( ) represents that the endpoint is not included in the interval. - The symbol infinity (∞) represents an unbounded interval.

Let's represent the intervals on a number line:

         -7         0         5         10
          |---------|---------|---------|

The interval [-7; 5) includes all real numbers from -7 up to (but not including) 5. We use a closed square bracket at -7 to indicate that -7 is included in the interval, and a round bracket at 5 to indicate that 5 is not included in the interval.

The interval (infinity; 10] includes all real numbers greater than 10. We use a round bracket at infinity to indicate that infinity is not included in the interval, and a closed square bracket at 10 to indicate that 10 is included in the interval.

Intersection and Union of Intervals

To find the intersection and union of the intervals [-7; 5) and (infinity; 10], we need to determine the common elements between the two intervals.

The intersection of two intervals is the set of elements that are common to both intervals. In this case, since the intervals do not overlap, their intersection is an empty set.

The union of two intervals is the set of elements that belong to either of the intervals. In this case, the union of the intervals [-7; 5) and (infinity; 10] includes all real numbers from -7 up to (but not including) 5, as well as all real numbers greater than 10.

Therefore, the intersection of the intervals [-7; 5) and (infinity; 10] is an empty set, and the union is the set of all real numbers from -7 up to (but not including) 5, as well as all real numbers greater than 10.

I hope this helps! Let me know if you have any further questions.