Math Problem Statement

Identify the shaded area in the given Venn diagram.

Solution

The diagram shows two sets, labeled A and B, within a universal set (the rectangle). The shaded area corresponds to the region outside of set AA, while it still includes some parts of set BB.

This shaded area is represented by AA', which means "not A" or the complement of set AA. Hence, the correct answer is:

  • A'.

Would you like further clarification on Venn diagrams or set operations?

Here are some related questions:

  1. What is the complement of a set in set theory?
  2. How do you represent the union of two sets in a Venn diagram?
  3. What does ABA \cap B (intersection of two sets) represent in a Venn diagram?
  4. Can a Venn diagram have more than two sets? How does it change visually?
  5. What does the shaded region in a Venn diagram represent mathematically?

Tip: The complement of a set AA, denoted AA', includes everything in the universal set except the elements of AA.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Venn Diagrams
Complements of Sets

Formulas

A' = Universal Set - A (Complement of Set A)

Theorems

Set Complement Theorem
Union and Intersection in Set Theory

Suitable Grade Level

Grades 9-12