Math Problem Statement

Let S be the universal set, where: S = /1, 2,3,.. 23,24, 25] Let sets A and B be subsets of S, where: set A = /3, 4, 7, 9, 11, 14, 15, 17, 18, Set B N f9, 12, 14, 18, 19, 20, 21, 23, 24, 25) Find the number of elements in the set (A U B)

Solution

To find the number of elements in the set ABA \cup B (the union of sets AA and BB), we need to determine all unique elements in either set AA, set BB, or both.

Given Sets:

  • A={3,4,7,9,11,14,15,17,18}A = \{ 3, 4, 7, 9, 11, 14, 15, 17, 18 \}
  • B={9,12,14,18,19,20,21,23,24,25}B = \{ 9, 12, 14, 18, 19, 20, 21, 23, 24, 25 \}

Step-by-Step Process:

  1. List all elements in ABA \cup B (the union of AA and BB):
    The union operation combines all elements in both sets without duplicates: AB={3,4,7,9,11,12,14,15,17,18,19,20,21,23,24,25}A \cup B = \{ 3, 4, 7, 9, 11, 12, 14, 15, 17, 18, 19, 20, 21, 23, 24, 25 \}

  2. Count the unique elements:
    Now we count the number of unique elements in this union set: Number of elements in AB=16\text{Number of elements in } A \cup B = 16

Final Answer:

The number of elements in ABA \cup B is 16.

Would you like a detailed breakdown of how to find ABA \cap B (intersection) or any other aspects?

Here are some follow-up questions related to set theory:

  1. What is the number of elements in the set ABA \cap B (intersection of sets AA and BB)?
  2. What is the number of elements in the set ABA \setminus B (elements in AA but not in BB)?
  3. How do we find the number of elements in the set S(AB)S \setminus (A \cup B) (complement of the union)?
  4. What is the difference between ABA \cup B and ABA \cap B?
  5. How can we find the symmetric difference between sets AA and BB?

Tip: When dealing with unions and intersections, organizing elements carefully and removing duplicates will help avoid mistakes!

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Math Problem Analysis

Mathematical Concepts

Set Theory
Union of Sets

Formulas

|A ∪ B| = |A| + |B| - |A ∩ B|

Theorems

Union of Sets Theorem

Suitable Grade Level

Grades 6-8