Math Problem Statement

If   BAnAnUn  ,7)(,25)'(,58)(  BAn   Bn 

Solution

It seems like the symbols in your question didn’t render properly. Let’s break it down and try to reconstruct the problem.

If we assume the question involves sets AA and BB, with various set operations, it could look something like this:

Given:

  • n(A)=58n(A) = 58 (the number of elements in set AA)
  • n(B)=25n(B') = 25 (the number of elements in the complement of set BB, i.e., elements not in BB)
  • n(AB)=7n(A \cap B) = 7 (the number of elements common to both sets AA and BB)

You are likely looking to calculate n(AB)n(A \cup B) or perhaps other quantities involving the union or intersection of sets.

Formula:

To calculate the number of elements in the union of two sets, ABA \cup B, we can use the following equation:

n(AB)=n(A)+n(B)n(AB)n(A \cup B) = n(A) + n(B) - n(A \cap B)

Since you are given n(B)=25n(B') = 25, we can find n(B)n(B) using:

n(B)=n(U)n(B)n(B) = n(U) - n(B')

Where n(U)n(U) is the total number of elements in the universal set. If you know n(U)n(U), we can proceed with the calculation.

Would you be able to clarify or provide more details about the universal set, or any missing information? I’ll also guide you through solving once we have all necessary data.


Expansion Questions:

  1. What is the total number of elements in the universal set UU?
  2. Do we have additional details on the relation between sets AA and BB?
  3. Are there any restrictions or special properties for sets AA and BB?
  4. Is the problem asking for other quantities beyond n(AB)n(A \cup B)?
  5. Are you familiar with Venn diagrams for solving such set problems?

Tip: Always confirm whether you're dealing with finite or infinite sets when applying these formulas.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Union and Intersection of Sets
Complement of Sets

Formulas

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
n(B) = n(U) - n(B')

Theorems

Inclusion-Exclusion Principle

Suitable Grade Level

Grades 9-12