Math Problem Statement

If A = {7, 8} and B = {2, 4, 6}

Solution

It seems like you are defining two sets, AA and BB, but there is no specific question attached. Let's explore a few operations that can be performed with these sets:

  1. Union: The union of sets AA and BB is the set of all elements that are in AA, in BB, or in both. AB={2,4,6,7,8}A \cup B = \{2, 4, 6, 7, 8\}

  2. Intersection: The intersection of sets AA and BB is the set of elements that are in both AA and BB. Since there are no common elements: AB=A \cap B = \emptyset

  3. Difference: The difference ABA - B (elements in AA but not in BB) is: AB={7,8}A - B = \{7, 8\} And the difference BAB - A (elements in BB but not in AA) is: BA={2,4,6}B - A = \{2, 4, 6\}

  4. Cartesian Product: The Cartesian product A×BA \times B is the set of all ordered pairs where the first element is from AA and the second is from BB: A×B={(7,2),(7,4),(7,6),(8,2),(8,4),(8,6)}A \times B = \{(7, 2), (7, 4), (7, 6), (8, 2), (8, 4), (8, 6)\}

Let me know if you have any specific operations or questions related to these sets, or if you'd like further details.

Relative Questions:

  1. What is the union of two sets and how is it useful in set theory?
  2. How can we find the Cartesian product of sets, and what are its applications?
  3. What is the difference between set intersection and set union?
  4. How do you interpret an empty set result in an intersection?
  5. How does the difference operation work between two sets?

Tip: When working with sets, remember that the order of elements in the set does not matter, but each element must be unique.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Set Operations

Formulas

Union: A ∪ B = {2, 4, 6, 7, 8}
Intersection: A ∩ B = ∅
Difference: A - B = {7, 8}, B - A = {2, 4, 6}
Cartesian Product: A × B = {(7, 2), (7, 4), (7, 6), (8, 2), (8, 4), (8, 6)}

Theorems

Basic Set Theory Theorems

Suitable Grade Level

Grades 8-10