UPSKILL MATH PLUS

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**Sets can be expressed in three ways**:

- The set of all even natural numbers.
- Set \(A =\) {\(x | x\) is an even natural number}.
- Set \(A =\) $\left\{2,\phantom{\rule{0.147em}{0ex}}4,\phantom{\rule{0.147em}{0ex}}6,\phantom{\rule{0.147em}{0ex}}8,\phantom{\rule{0.147em}{0ex}}10,\left....\right\}\right.$.

All the above lines represent the same meaning in different forms.

Thus, a set can be represented in any one of the following ways.

- Descriptive form.
- Set builder form/Ruler form.
- Roster form/Tabular form.

A set is described in words is called descriptive form.

- The set of odd natural numbers less than \(20\).
- The set of all first four months of the year.

A rule describes all the elements is called a set builder or ruler form.

- $A\phantom{\rule{0.147em}{0ex}}=\left\{x:x\phantom{\rule{0.147em}{0ex}}\mathit{is}\phantom{\rule{0.147em}{0ex}}\mathit{an}\phantom{\rule{0.147em}{0ex}}\mathit{odd}\phantom{\rule{0.147em}{0ex}}\mathit{natural}\phantom{\rule{0.147em}{0ex}}\mathit{and}\phantom{\rule{0.147em}{0ex}}\left.x<20\right\}\right.$
- $B=\left\{x|x\phantom{\rule{0.147em}{0ex}}\mathit{is}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{first}\phantom{\rule{0.147em}{0ex}}\mathit{four}\phantom{\rule{0.147em}{0ex}}\mathit{months}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\left.\mathit{year}\right\}\right.$

A set is described by listing all the elements of it that are called as a Roster form.

- $A\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\left\{1,\phantom{\rule{0.147em}{0ex}}3,\phantom{\rule{0.147em}{0ex}}5,7,9,11,13,15,17,\left.19\right\}\right.$
- $B=\phantom{\rule{0.147em}{0ex}}\left\{\mathit{January},\phantom{\rule{0.147em}{0ex}}\mathit{February},\phantom{\rule{0.147em}{0ex}}\mathit{March},\left.\phantom{\rule{0.147em}{0ex}}\mathit{April}\right\}\right.$