Question

2. Write the following sets in tabular form.
a) {x: x = 2n, ne N and x < 10}​

Answer 1

Answer :

A = { 2 , 4 , 6 , 8 }

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 :

The given set (in set builder form) is ;

A = { x : x = 2n , n € N and x < 10 }

★ If n = 1

=> x = 2n

=> x = 2×1

=> x = 2

★ If n = 2

=> x = 2n

=> x = 2×2

=> x = 4

★ If n = 3

=> x = 2n

=> x = 2×3

=> x = 6

★ If n = 4

=> x = 2n

=> x = 2×4

=> x = 8

Hence ,

The given set in tabular form will be;

A = { 2 , 4 , 6 , 8 }

Note : If we would have taken n = 5 , then

x = 2n

x = 2×5

x = 10

But we have to choose x < 10 .

Thus , we chose x = 2n for n = 1 , 2 , 3 , 4 .

Hence ,

A = { 2 , 4 , 6 , 8 }