Question
Describe the following sets in Roster form:
$\{1, 4, 9, 16, ..., 100\};$
$\{1, 4, 9, 16, ..., 100\};$
✓
Answer
In set Builder form, a set s described by some characterising property $P (x)$ of its elements x. In this case a set can be described as $\{x: P(x)$ hold$\}$ which is read as 'the set of all $x$ such that $P (x)$ holds'. The symbols $':'$ or $'I'$ is read as 'such that'.
As $1^2 = 1$
$2^2 = 4$
$3^2 = 9$
$:$
$:$
$10^2 = 100$
$\therefore$ The above set may be described as $\{\text{x}^2 : \text{x} \in \text{N 8c } 1 \leq\text{ x} \leq{ 10}\}.$
As $1^2 = 1$
$2^2 = 4$
$3^2 = 9$
$:$
$:$
$10^2 = 100$
$\therefore$ The above set may be described as $\{\text{x}^2 : \text{x} \in \text{N 8c } 1 \leq\text{ x} \leq{ 10}\}.$
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