Math Problem Statement
',
Solution
The problem is asking to evaluate the expression where and are two sets.
Explanation:
- represents the intersection of sets and , i.e., the set of elements that are in both and .
- represents the union of with the intersection of and .
Now, consider the following logic:
- Every element of is already in , since the intersection is a subset of .
- Therefore, the union of with will simply give back the set because all elements of are already included in .
Thus, we conclude:
The correct answer is .
Would you like more details on set operations or related concepts?
Here are 5 follow-up questions:
- What is the difference between the union and intersection of two sets?
- Can you give an example where ?
- How would you prove that using set properties?
- What happens to the union and intersection if and are disjoint sets?
- Can the union of two sets ever result in a set smaller than the individual sets?
Tip: Remember that the union of two sets includes all elements from both and , while the intersection includes only the common elements.
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Math Problem Analysis
Mathematical Concepts
Set Theory
Union and Intersection of Sets
Formulas
X ∪ (X ∩ Y) = X
Theorems
Subset Theorem
Distributive Law of Sets
Suitable Grade Level
Grades 9-12
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