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 (the union of sets and ), we need to determine all unique elements in either set , set , or both.
Given Sets:
Step-by-Step Process:
-
List all elements in (the union of and ):
The union operation combines all elements in both sets without duplicates: -
Count the unique elements:
Now we count the number of unique elements in this union set:
Final Answer:
The number of elements in is 16.
Would you like a detailed breakdown of how to find (intersection) or any other aspects?
Here are some follow-up questions related to set theory:
- What is the number of elements in the set (intersection of sets and )?
- What is the number of elements in the set (elements in but not in )?
- How do we find the number of elements in the set (complement of the union)?
- What is the difference between and ?
- How can we find the symmetric difference between sets and ?
Tip: When dealing with unions and intersections, organizing elements carefully and removing duplicates will help avoid mistakes!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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