Question

x:x is a multiple of2 change into set builder form

Answer 1

Answer :

A = { x : x = 2n , n € N }

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 is :

" Set of multiples of 2 "

Let the given set be A .

Thus ,

The given set in roster form will be ;

A = { 2 , 4 , 6 , 8 , . . . }

Now ,

The given set in set builder form will be ;

A = { x : x = 2n , n € N }

Hence ,

Required answer is { x : x = 2n , n € N }