Math Problem Statement
Solution
The problem requires finding the region that represents , where:
- is the intersection of sets and (the area common to both and ).
- represents the complement of , meaning the area outside set .
To solve this:
- First, locate the region where sets and overlap. This is the intersection area between the two circles and .
- Next, find the part of this intersection that is outside set . This excludes any part of that also intersects with .
In the Venn diagram provided, the correct region to select will be the portion of the intersection that lies outside .
From the image, this corresponds to the section in the middle that overlaps between and but does not intersect with . This should be only one region on the diagram.
Would you like more detailed steps or have specific questions?
Here are some related questions:
- How would the shaded region change if the set were instead?
- What area would represent in the same diagram?
- How is different in terms of shading compared to ?
- How would you represent the union in a Venn diagram?
- What would the region look like for ?
Tip: Always identify each region individually and then combine based on the intersection or union required by the problem.
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Math Problem Analysis
Mathematical Concepts
Set Theory
Intersection
Complement
Formulas
\( A \cap B \cap C^c \) represents the intersection of A and B and the complement of C
Theorems
-
Suitable Grade Level
Grades 9-12