Question

B. Write Q = { x | x= n/2; 0 < n <_ 5 and n € N}
in roster form.​

Answer 1

Question :

Write Q = { x | x = n/2 ; 0 < n ≤ 5 ; n € N } in roster form .

Answer :

Q = { 1/2 , 1 , 3/2 , 2 , 5/2 }

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 ;

Q = { x | x = n/2 ; 0 < n ≤ 5 ; n € N }

Now ,

Let's find the elements of set Q .

→ If 0 < n ≤ 5 and n € N , then ;

n = 1 , 2 , 3 , 4 , 5 .

• If n = 1 , then ;

x = n/2 = 1/2

• If n = 2 , then ;

x = n/2 = 2/2 = 1

• If n = 3 , then ;

x = n/2 = 3/2

• If n = 4 , then ;

x = n/2 = 4/2 = 2

• If n = 5 , then ;

x = n/2 = 5/2

Hence ,

The given set in roster form will be ;

Q = { 1/2 , 1 , 3/2 , 2 , 5/2 }