Question

Write the set in​ set-builder notation.
​{1,3,5,7,9​}
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Part 1
Choose the correct answer below.
A.
​{x | 1less than or equalsxless than or equals9​}
B.
​{x | x is a natural​ number, xless than or equals9​}
C.
​{x | x is odd​, x is a natural​ number}
D.
​{x | x is odd​, x is a natural​ number, xgreater than or equals1​}
E.
​{x | x is​ odd, xless than or equals9​}
F.
​{x | x is odd​, x is a natural​ number, xless than or equals9​}

Answer 1

The set \(\{1, 3, 5, 7, 9\}\) can be described in set-builder notation by identifying the properties that define its elements.

The elements of the set are odd natural numbers that are less than or equal to 9. Therefore, the correct set-builder notation that captures these properties is:

**D.** \(\{x \, | \, x \text{ is odd}, x \text{ is a natural number}, x \geq 1\}\)

This option correctly specifies that the elements are odd, natural numbers, and meet the condition \(x \geq 1\).

Option F is also correct in that it specifies the elements as odd natural numbers with an upper bound of 9, but does not explicitly note that they start from 1, which makes it less precise than option D in capturing the exact set.

So, the best answer is D.