Math Problem Statement
Solution
To solve this problem, let's summarize the given data and apply the formula for the union of two sets.
Given Information
- : the total number of elements in the universal set .
- : the number of elements in set .
- : the number of elements in set .
- : the number of elements in the complement of .
We are asked to find , the number of elements in the intersection of sets and .
Steps to Solution
-
Calculate : Since , this means that there are 15 elements outside . Therefore:
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Use the Formula for the Union of Two Sets: We know that: Substituting the values we have:
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Solve for :
Answer
The value of is 29. Thus, the correct option is:
- a. 29
Would you like a detailed breakdown of the formula used or further examples?
Related Questions
- What is the concept of the universal set in set theory?
- How is the complement of a union calculated in set theory?
- What other methods could be used to find ?
- How can Venn diagrams help visualize this type of problem?
- What are real-world applications of calculating intersections in sets?
Tip
Always verify your set notation and total counts carefully to avoid simple errors in problems involving unions and intersections.
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Math Problem Analysis
Mathematical Concepts
Set Theory
Union and Intersection of Sets
Complement of a Set
Formulas
n(X ∪ Y) = n(X) + n(Y) - n(X ∩ Y)
n((X ∪ Y)') = n(U) - n(X ∪ Y)
Theorems
Principle of Inclusion-Exclusion
Suitable Grade Level
Grades 10-12
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