Question

c={t|t³=t,t€r} write it in roster nethod​

Answer 1

Answér :

C = { -1 , 0 , 1 }

Note :

★ Set : A well defined collection of distinct objects is called a set .

★ Cardinal number / Cardinality : The number of elements/members/objects in a finite set is called cardinal no. / Cardinality .

→ Cardinal no. of a finite set A is denoted by n(A) .

★ Method of representing a set :

a). Roster / Tabular / Listed form

b). Set Builder form

★ Roster form :

→ All elements are listed .

→ Elements are separated by commas .

→ Elements are enclosed within braces { } .

→ The order of writing elements doesn't matter .

→ The elements are not repeated

★ Set builder form :

→ The common properties of elements are written .

→ The elements is described using symbols like x , y , z (mostly x) .

→ Whole description of the elements are enclosed within braces { } .

Solution :

Here ,

The given set in set builder form is ;

C = { t | t³ = t , t € R } .

Let's find the elements of given set C .

Thus ,

=> t³ = t

=> t³ - t = 0

=> t(t² - 1) = 0

=> t(t + 1)(t - 1) = 0

=> t = 0 , -1 , 1 .

Hence , C = { -1 , 0 , 1 } .