UPSKILL MATH PLUS

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### Theory:

Sets can be expressed in three ways:
1. The set of all even natural numbers.
2. Set $$A =$$ {$$x | x$$ is an even natural number}.
3. 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,...}\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.
1. Descriptive form.
2. Set builder form/Ruler form.
3. Roster form/Tabular form.
A set is described in words is called descriptive form.
1. The set of odd natural numbers less than $$20$$.
2. The set of all first four months of the year.
A rule describes all the elements is called a set builder or ruler form.
1. $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}}x<20}\right\$
2. $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}}\mathit{year}}\right\$
A set is described by listing all the elements of it that are called as a Roster form.
1. $A\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\left\{1,\phantom{\rule{0.147em}{0ex}}3,\phantom{\rule{0.147em}{0ex}}5,7,9,11,13,15,17,19}\right\$
2. $B=\phantom{\rule{0.147em}{0ex}}\left\{\mathit{January},\phantom{\rule{0.147em}{0ex}}\mathit{February},\phantom{\rule{0.147em}{0ex}}\mathit{March},\phantom{\rule{0.147em}{0ex}}\mathit{April}}\right\$