Math Problem Statement

Which of these Venn diagrams show the complement of
B shaded? Figure 1

Solution

The complement of B, denoted as BB', consists of all the elements that are not in set B. In a Venn diagram, this means the area that is outside of circle B should be shaded, while the region inside B remains unshaded.

In the Venn diagram that shows the complement of B, the entire region outside of circle B, including any space outside B or shared by other sets (like set A if present), will be shaded. The inside of circle B will remain unshaded.

Here’s how you can identify the correct diagram:

  1. Look for the diagram where the area outside circle B (not inside it) is shaded.
  2. The area inside the circle representing B should be left unshaded.
  3. Any other sets (like A) present in the diagram should also be shaded where they do not overlap with B.

Do you want me to provide further details or explanations?

Here are 5 related questions to consider:

  1. How do we represent the union of two sets A and B in a Venn diagram?
  2. How can we visually represent the intersection of sets A and B?
  3. What does the complement of set A look like in a Venn diagram?
  4. How do we express the complement of both sets A and B in a Venn diagram?
  5. What does ABA \cup B complement look like in a Venn diagram?

Tip: When analyzing Venn diagrams, always focus on whether the shaded or unshaded regions correspond to the set(s) in question.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Venn Diagrams
Complement of a Set

Formulas

B' = Universal Set - B

Theorems

Complement Theorem

Suitable Grade Level

Grades 6-8