Math Problem Statement

(A ∩ B') ∪ C venn diagram

Solution

To represent the expression (AB)C(A \cap B') \cup C in a Venn diagram, let’s break it down:

  1. ABA \cap B': This represents the intersection of set A with the complement of set B. In other words, this includes all elements that are in A but not in B.

    • The complement of B, denoted as BB', includes everything that is not in B.
    • ABA \cap B' includes all elements in A that are outside of B.
  2. (AB)C(A \cap B') \cup C: This represents the union of the set ABA \cap B' with C.

    • The union means that all elements from both sets ABA \cap B' and CC are included.
    • So, in this case, we take everything that’s in A but not in B, and everything that’s in C, and combine them.

Venn Diagram Breakdown:

  • AA: A circle representing elements in set A.
  • BB: A circle representing elements in set B.
  • CC: A circle representing elements in set C.
  • ABA \cap B': The part of circle A that doesn't overlap with circle B.
  • (AB)C(A \cap B') \cup C: This includes the area of ABA \cap B' plus the entire circle C.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Venn Diagrams
Set Operations

Formulas

(A ∩ B') ∪ C

Theorems

Union and Intersection of Sets
Complement of a Set

Suitable Grade Level

Grades 8-10