Question

The roster form of the set $\{x:x=2r+3,\text{where}rϵI\text{and}-2<r\le 3\}$.

• A. $\{0,1,3,5,7\}$
• B. $\{1,3,5,7,9\}$
• C. $\{0,1,3,5,7,9\}$
• D. $\{1,3,5,7\}$

Answer 1

The correct option is B

$\{1,3,5,7,9\}$

Given $-2<r\le 3$ and $rϵI$

So, r = -1, 0, 1, 2, 3. Also $x=2r+3$

Substituting r = -1, 0, 1, 2, 3 we get,

$x=2(-1)+3=1$

$x=2\left(0\right)+3=3$

$x=2\left(1\right)+3=5$

$x=2\left(2\right)+3=7$

$x=2\left(3\right)+3=9$

$\therefore$ The set is {1, 3, 5, 7, 9}.