Math Problem Statement

Define the sets A, B, C, and D as shown. Mark all answers that are elements of (A ∩ B) ∪ C.

Solution

We are asked to find the elements of (AB)C(A \cap B) \cup C from the Venn diagram provided.

Step-by-Step Breakdown:

  1. Intersection ABA \cap B: This refers to the elements that are in both sets AA and BB. From the diagram, the only common element in both AA and BB is p.

  2. Set CC: From the diagram, the elements in set CC are s, m, and a.

  3. Union: The union of ABA \cap B and CC means we take all elements from both sets, i.e. (AB)C={p,s,m,a}(A \cap B) \cup C = \{p, s, m, a\}

Final Answer:

The elements of (AB)C(A \cap B) \cup C are p, s, m, and a.

Would you like further details on this solution or have any questions?

Here are 5 related questions to explore:

  1. What is the difference between the union and intersection of sets?
  2. How do we find the complement of a set in a Venn diagram?
  3. Can you explain what ABA \cup B would represent in this diagram?
  4. How can Venn diagrams be used to solve probability problems?
  5. What is the symmetric difference of two sets, and how is it represented in a Venn diagram?

Tip: When working with Venn diagrams, always analyze intersections and unions step by step to avoid missing elements.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Venn Diagrams
Union and Intersection of Sets

Formulas

Intersection of sets: A ∩ B
Union of sets: A ∪ B

Theorems

Union and Intersection Theorem

Suitable Grade Level

Grades 6-9