Math Problem Statement

Let U= {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 5}, C = {3, 4, 6}. List all the members of the following:

A ∩ C =

Solution

The intersection of two sets, ACA \cap C, includes all the elements that are present in both set AA and set CC.

Given:

  • A={1,2,3,5}A = \{1, 2, 3, 5\}
  • C={3,4,6}C = \{3, 4, 6\}

The common element between these two sets is 33.

Thus, AC={3}A \cap C = \{3\}.

Would you like further details or have any questions?

Here are 5 related questions to further explore set theory:

  1. What is ACA \cup C (the union of AA and CC)?
  2. What is AA', the complement of AA in UU?
  3. How can we find (AC)(A \cup C)', the complement of ACA \cup C?
  4. What is the result of ACA \setminus C (the difference between AA and CC)?
  5. How does the concept of a universal set UU influence set operations?

Tip: When dealing with sets, intersections focus on common elements, while unions combine all distinct elements from the sets involved.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Intersection of Sets

Formulas

A ∩ C = {x | x ∈ A and x ∈ C}

Theorems

Intersection of Sets Theorem

Suitable Grade Level

Grades 6-8