Math Problem Statement

Which Region/s is/are shaded in (C ∪ A) ∩ B?

Solution

The given question asks to identify the region shaded in (CA)B(C \cup A) \cap B on the Venn diagram.

To break this down:

  1. CAC \cup A: This represents the union of sets CC and AA. This includes all regions that belong to either CC or AA or both. From the Venn diagram, this includes regions: I, II, IV, V, VI, VII.

  2. BB: This represents all the regions that belong to set BB. From the diagram, the regions in BB are: II, III, V, VI.

  3. Intersection (CA)B(C \cup A) \cap B: This represents the overlap between CAC \cup A and BB, which means we are looking for the regions that are common to both sets. These common regions are: II, V, VI.

Thus, the regions shaded in (CA)B(C \cup A) \cap B are II, V, and VI.

Do you need further details or clarifications on this?

Here are five related questions to deepen your understanding:

  1. What does ABA \cap B represent in a Venn diagram?
  2. How would the regions change if we asked for CBC \cap B?
  3. What is the union ABCA \cup B \cup C in the diagram?
  4. Can you identify the region representing ABA \setminus B?
  5. How would (AB)C(A \cup B) \setminus C be represented?

Tip: The union of sets includes all elements from both sets, while the intersection includes only the elements common to both sets.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Venn Diagrams
Unions and Intersections

Formulas

(C ∪ A) ∩ B
Union (C ∪ A): All regions in either set C or A
Intersection (C ∪ A) ∩ B: Overlapping regions between (C ∪ A) and B

Theorems

Intersection of Sets
Union of Sets

Suitable Grade Level

Grades 8-10