Question

Use set notation to write the members of the following set, or state that the set has no members. Odd numbers between 2 and 82 that are multiples of 9

Answer 1

Let the set of all Odd multiples of 9 between 2 and 82 be denoted by D, then, using set-builder notation,

$D=\{ 18n+9 \mid n \in \mathbb{N}, 0\le n\le 4 \}$

The odd multiples of 9, $m$, in the range $2\le m \le 82$ form the set

$\{9,27,45,63,81\}$

Each member of the set is a term of the arithmetic progression

$U_n=18n+9$

where the values of $n$ range from 0 to 4, or $0\le n\le 4$

Putting these facts together, we get the result

$D=\{ 18n+9 \mid n \in \mathbb{N}, 0\le n\le 4 \}$

Learn more about set-builder notation here: brainly.com/question/17238769