Example Question - set-builder notation
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Writing Sets of Multiples in Roster and Set-Builder Notations
<p>To find all multiples of \(3\) between \(1\) and \(20\), we list the multiples within this range.</p> <p>Roster form: \(\{3, 6, 9, 12, 15, 18\}\)</p> <p>To express this set in set-builder notation, we define the properties that all elements of the set share. All elements \(x\) are multiples of \(3\), hence \(x = 3n\) for some integer \(n\), and \(x\) is greater than \(1\) and less than or equal to \(20\).</p> <p>Set-builder form: \(\{x \mid x = 3n, n \in \mathbb{Z}, 1 < x \leq 20\}\)</p>
Conversion between Roster Form and Set-Builder Notation
<p>\begin{align*} A &= \{1, 3, 5, 7, 9\} \text{ in set-builder notation is } A = \{ x | x \text{ is an odd number less than 10} \}. \end{align*}</p> <p>\begin{align*} B &= \{a, e, i, o, u\} \text{ in set-builder notation is } B = \{ x | x \text{ is a vowel in the English alphabet} \}. \end{align*}</p> <p>\begin{align*} C &= \{2, 4, 6, 8, 10\} \text{ in set-builder notation is } C = \{ x | x \text{ is an even number less than or equal to 10} \}. \end{align*}</p> <p>\begin{align*} D &= \{x | x \text{ is a prime number less than 10}\} \text{ in roster form is } D = \{2, 3, 5, 7\}. \end{align*}</p> <p>\begin{align*} E &= \{10, 20, 30, 40, 50\} \text{ in set-builder notation is } E = \{ x | x = 10n, n \in \mathbb{N}, 1 \leq n \leq 5 \}. \end{align*}</p>
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