Math Problem Statement

Indicate where the given set A^C ∩ B is located on the figure by clicking the boxes within regions that should be shaded.

Solution

To solve this problem, we need to identify the region representing ACBA^C \cap B in the Venn diagram.

  1. Understanding ACA^C: ACA^C represents the complement of set AA. This is the region outside of AA.

  2. Understanding BB: Set BB is the right circle, and it includes everything inside that circle.

  3. Intersection ACBA^C \cap B: The intersection of ACA^C and BB will be the area that is within BB but outside of AA.

From the diagram, this corresponds to the part of circle BB that does not overlap with circle AA.

Solution:

The shaded region should be the part of BB that is outside of AA. This is usually the right part of the BB circle that does not overlap with AA.

Would you like a detailed step-by-step breakdown of how this solution was reached, or do you have any other questions?

Related Questions:

  1. What would the region ABA \cap B look like on this Venn diagram?
  2. How would you represent ACBCA^C \cap B^C on the Venn diagram?
  3. If the expression was ABA \cup B, which regions would be shaded?
  4. What does (AB)C(A \cap B)^C represent, and how would it appear on the Venn diagram?
  5. How would you depict ABCA \cup B^C in a similar Venn diagram?

Tip: When working with Venn diagrams, it can be helpful to shade each part of the set operations individually first and then combine them.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Set Theory
Complement of a Set
Intersection of Sets
Venn Diagrams

Formulas

A^C: Complement of set A
A^C ∩ B: Intersection of A complement and B

Theorems

Properties of Sets
Intersection and Complement Rules

Suitable Grade Level

Grades 9-12