Question

Write the set A = { 1491625 }in the set-builder form.

Answer 1

Answer :

A = { x : x = n² , 1 ≤ n ≤ 5 , n € N }

Note :

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

★ 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 roster form ) is ;

A = { 1 , 4 , 9 , 16 , 25 }

The given set can be rewritten as ;

A = { 1² , 2² , 3² , 4² , 5² }

Observing the pattern , we can say that the elements of the given set A are the square of natural numbers .

Thus ,

The given set A in set builder form will be ;

A = { x : x = n² , 1 ≤ n ≤ 5 , n € N }

Hence ,

A = { x : x = n² , 1 ≤ n ≤ 5 , n € N }