https://file.aiquickdraw.com/mathbot/file/1726134875378gn1b3orq.jpg

The sets provided are defined as follows:

- Set \( A \) consists of the absolute values of integers \(\{ -5, -6, -7, -8, -9 \}\). Thus, \( A = \{5, 6, 7, 8, 9\} \).
- Set \( B \) is described as \(\{ b \mid b = 5 \cdot m, m \in \mathbb{Z} \}\). This represents all multiples of 5, i.e., \(\{ \ldots, -10, -5, 0, 5, 10, \ldots \} \).

1) **Element in the intersection \( A \cap B \):**
   You've answered that \( a = -6 \) is in the intersection. However, this seems to be a mistake because the element \( -6 \) is not in \( A \) as defined by absolute values nor is it a multiple of 5. Instead, looking for positive elements from \( A \) that are multiples of 5, we find that the number 5 is the only element that meets these criteria. So, the correct element in the intersection \( A \cap B \) should be 5.

2) **Determining \( n \) such that the element is in the intersection:**
   You've answered \( n = -6 \). Since \( A \) consists of positive absolute values, \( n \) must be \(-5\) to make \( a = 5 \), which is a multiple of 5 and an element in both \( A \) and \( B \).

If you have any more questions or need further details, feel free to ask! Here are some follow-up questions you might consider:

1. Would you like to explore how other elements of set \( A \) compare with the multiples in set \( B \)?
2. How would the intersection change if we expanded the range of \( n \) in set \( A \)?
3. Are you interested in understanding how set notation works for other types of mathematical sets?
4. Do you want to solve problems involving set operations with different constraints?
5. Could you use a clarification on absolute values and how they relate to sets in general?

**Tip:** When verifying elements of an intersection between two sets, it is crucial to ensure the element satisfies all conditions described for each set.

Given two sets: A = {a | a = |n| - 1, n ∈ {-5, -6, -7, -8, -9}} and B = {b | b = 5 * m, m ∈ Z}. Find an element in the intersection A ∩ B and determine for which n the element belongs to A.

Solve a set theory problem involving two sets A and B. Set A is defined using absolute values and set B consists of multiples of 5. Learn how to find the intersection of these sets and determine the corresponding element for n.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation