Question

Найдите A U B, A ∩ B, A\B если A=(-5;8) и B=(3:11)

Answer 1

А U B (-5;11)

A пересечение В (3;8)

знак пересечение не нашла , извините

Answer 2

To find the union (A U B), intersection (A ∩ B), and set difference (A \ B) between sets A and B, we first need to understand the notation used to represent the sets. In the context of your question, A=(-5;8) and B=(3:11) are notations for intervals, not sets. We can rewrite these intervals in set notation to make the operations clearer.

The set A=(-5;8) includes all real numbers greater than -5 and less than 8, but excluding -5 and 8. In set notation, it can be represented as:

A = {x | -5 < x < 8}

Similarly, the set B=(3:11) includes all real numbers greater than 3 and less than 11, excluding 3 and 11:

B = {x | 3 < x < 11}

Now, let's perform the set operations:

1. Union (A U B): The union of two sets A and B includes all the elements that are in either A or B or both.

A U B = {x | x ∈ A or x ∈ B}

To find the union, we need to consider all numbers that satisfy the conditions of either A or B:

A U B = {x | -5 < x < 8 or 3 < x < 11}

Since both sets are intervals, we can express the union as a single interval:

A U B = {x | -5 < x < 11}

2. Intersection (A ∩ B): The intersection of two sets A and B includes all the elements that are common to both A and B.

A ∩ B = {x | x ∈ A and x ∈ B}

To find the intersection, we need to consider all numbers that satisfy the conditions of both A and B:

A ∩ B = {x | -5 < x < 8 and 3 < x < 11}

Since the sets A and B have no common elements, their intersection is an empty set:

A ∩ B = ∅

3. Set Difference (A \ B): The set difference of A and B includes all the elements that are in A but not in B.

A \ B = {x | x ∈ A and x ∉ B}

To find the set difference, we need to consider all numbers that satisfy the condition of A but not B:

A \ B = {x | -5 < x < 8 and (x ≤ 3 or x ≥ 11)}

Since the set B includes all numbers between 3 and 11, excluding 3 and 11 themselves, the set difference A \ B consists of all numbers in the interval (-5, 8) except for the interval (3, 11):

A \ B = {x | -5 < x < 3 or 8 < x < 11}

So, to summarize:

A U B = {x | -5 < x < 11} A ∩ B = ∅ A \ B = {x | -5 < x < 3 or 8 < x < 11}