Math Problem Statement
Consider the following sets:
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U=/x/x is a whole number from 0 to 20.
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X= /x/ x is a whole number less than 10
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Y=/x/x is a whole number greater than 5 but less than 20.
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Z=/x/x is a whole number between 4 and 11
Solution
Let's define the sets based on the information given:
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Set : The universal set consists of all whole numbers from 0 to 20.
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Set : This set consists of whole numbers less than 10.
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Set : This set consists of whole numbers greater than 5 but less than 20.
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Set : This set consists of whole numbers between 4 and 11 (including 4 and 11).
Would you like to perform specific operations with these sets, such as union, intersection, or difference?
Here are 5 follow-up questions related to set theory:
- What is (the union of sets and )?
- What is (the intersection of sets and )?
- What is the complement of set with respect to (denoted )?
- How many elements are in the union of all three sets , , and ?
- What is the symmetric difference between sets and ?
Tip: The union of two sets contains all distinct elements that are in either set, while the intersection contains only elements that are in both sets.
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Math Problem Analysis
Mathematical Concepts
Set Theory
Union of Sets
Intersection of Sets
Complement of Sets
Symmetric Difference
Formulas
Union of sets: X ∪ Y
Intersection of sets: X ∩ Y
Complement of sets: U - Z
Symmetric difference: (X ∪ Z) - (X ∩ Z)
Theorems
Set Union Theorem
Set Intersection Theorem
Complement Rule
Symmetric Difference Theorem
Suitable Grade Level
Grades 6-8
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