Math Problem Statement

Given the set, shade the indicated region. Show your solution in the answer sheet.

a) A intersection B to the power of apostrophe

Venn diagram 01

Solution

To solve this, let's analyze the given statement:

A ∩ B' (A intersection B') means:

  1. The elements must belong to A.
  2. The elements must NOT belong to B (B', or "B complement," is the set of elements outside B).

Solution Approach:

  1. Draw two overlapping circles representing sets A and B within a rectangle representing the universal set.
  2. Identify the region that represents A (inside the circle of A).
  3. Exclude the portion where A and B overlap (since we need to exclude B's region). The remaining part of A (outside the overlap with B) is A ∩ B'.

Venn Diagram Description:

The final shaded region will be the part of A that does not overlap with B. This is the "crescent-shaped" portion of A outside of B.


Would you like me to generate an image of the Venn Diagram to visualize the solution? Let me know! Here’s also how we can expand this concept. 😊


5 Related Questions:

  1. What is the difference between ABA \cap B and ABA \cap B'?
  2. How do you calculate ABA \cup B' (complement of A union B)?
  3. How does ABA - B relate to ABA \cap B'?
  4. Can you represent this set operation using set-builder notation?
  5. How would the solution change if the universal set is limited?

Tip: Always start solving set problems by visualizing or drawing a Venn diagram—it helps clarify regions effectively.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Venn Diagrams
Set Operations

Formulas

A ∩ B'

Theorems

Complement of a set
Intersection of sets

Suitable Grade Level

Grades 7-9