Math Problem Statement

Which Region/s is/are shaded in A ⋂ B ⋂ C ? I II III IV V VI VII VIII

Which Region/s is/are shaded in A ⋂ B ⋂ C?

Solution

The image shows a Venn diagram with three sets AA, BB, and CC along with their universal set UU. The regions are numbered I to VIII, and we are tasked with identifying the region or regions corresponding to ABCA \cap B \cap C, which represents the intersection of sets AA, BB, and CC.

The region where all three sets overlap is the central region of the diagram, which is marked as V. Therefore, the region that corresponds to ABCA \cap B \cap C is:

  • V (Region V)

Would you like more details or have any questions?

Here are five related questions to deepen your understanding:

  1. What is the meaning of ABCA \cup B \cup C in this Venn diagram?
  2. Which regions represent ABA \cap B, but not CC?
  3. Can you identify the regions representing only CC (i.e., C(AB)C - (A \cup B))?
  4. What does (AB)c(A \cap B)^c, the complement of ABA \cap B, correspond to in this diagram?
  5. How would you represent AcBcCcA^c \cup B^c \cup C^c, the complement of all sets?

Tip: In Venn diagrams, the overlap of sets visually represents intersections.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Venn Diagrams
Intersection of Sets

Formulas

A ⋂ B ⋂ C = Region common to A, B, and C

Theorems

Intersection Theorem

Suitable Grade Level

Grades 6-8