Question

Для множества А=[1;5),B=[4:6] и C=(-3;2] найдите множество (A U B) C. Ответ нужен полностью расписанный

Answer 1

Рисуешь множества А и В на одной координатной прямой. Одно сверху, другое снизу. Там, где они совпадают, результирующее множество. Итого, ответ должен получиться: от 4 (включительно) до 5 (не включительно)

Answer 2

Calculating the Union of Sets A, B, and C

To find the union of sets A, B, and C, we need to first understand the notation used for the sets. The notation A=[1;5) represents the set A as all real numbers greater than or equal to 1 and less than 5. The notation B=[4:6) represents the set B as all real numbers greater than or equal to 4 and less than 6. The notation C=(-3;2] represents the set C as all real numbers greater than -3 and less than or equal to 2.

Calculating A U B

The union of sets A and B, denoted as A U B, is the set of all elements that are in A, in B, or in both A and B.

The union of A and B can be calculated as: A U B = {x | x ∈ A or x ∈ B}

Given: - A=[1;5) - B=[4:6)

The union of A and B, A U B, is the set of all real numbers greater than or equal to 1 and less than 6.

Calculating (A U B) U C

Now, we need to find the union of the set (A U B) and C.

Given: - A U B = {x | 1 ≤ x < 6} - C=(-3;2]

The union of (A U B) and C, denoted as (A U B) U C, is the set of all elements that are in (A U B), in C, or in both (A U B) and C.

The union of (A U B) and C can be calculated as: (A U B) U C = {x | x ∈ (A U B) or x ∈ C}

By combining the ranges of A U B and C, we get: (A U B) U C = {x | -3 < x < 6}

Therefore, the set (A U B) U C is all real numbers greater than -3 and less than 6.

So, (A U B) U C = (-3;6).