Math Problem Statement
Solution
The question asks to express the set of even natural numbers in set-builder notation.
Let’s go through the options:
-
A:
This represents the odd natural numbers, which is not correct. -
B:
This represents the odd integers, which is also incorrect. -
C:
This represents all natural numbers, not specifically the even ones, so this is incorrect. -
D:
This represents the natural numbers that are multiples of 8, not all even numbers. Hence, it’s incorrect. -
E:
This is correct because it specifies the natural numbers that are even. -
F:
This represents an empty set, which is not correct.
Thus, the correct answer is E: .
Would you like further details or explanations on any part of the question? Here are some related questions for deeper understanding:
- What are the natural numbers () and how are they defined?
- How do we define even numbers in set theory?
- Can you describe how set-builder notation works with other types of numbers (e.g., odd numbers)?
- What is the difference between natural numbers and integers in set theory?
- How do we express other specific subsets of numbers, like prime numbers, using set-builder notation?
Tip: Remember that set-builder notation is a shorthand way of defining sets by specifying the properties that the members of the set must satisfy!
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Math Problem Analysis
Mathematical Concepts
Set Theory
Natural Numbers
Even Numbers
Formulas
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Theorems
Definition of natural numbers
Definition of even numbers in set theory
Suitable Grade Level
Grades 6-8
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