Question

how can we express set A={0,2,4,6,8} in set builder method?

Answer 1

Given set,

$A=\{0,\ 2,\ 4,\ 6,\ 8\}$

Here the elements in set A are non - negative even integers.

We know even integers can be expressed in the form 2n, for every integer n.

By this, we can express the elements as shown below.

→  0 = 2 × 0

→  2 = 2 × 1

→  4 = 2 × 2

→  6 = 2 × 3

→  8 = 2 × 4

Here the values of 'n' are 0, 1, 2, 3, 4.

We can mention 'n' as 'n' lies among the whole numbers but n is less than or equal to 4, or we can say 'n' is less than 5. No need to mention 'n' is greater than or equal to 0, because the set of whole numbers contains integers greater than or equal to 0.

So we can write set A in set builder form as either the following:

$\Longrightarrow\ A=\{x:x=2n,\ n\in\mathbb{W},\ n\leq 4\}\\ \\ \Longrightarrow\ A=\{x:x=2n,\ n\in\mathbb{W},\ n<5\}$

Or simply we write either the following:

$\Longrightarrow\ A=\{2x:x\in\mathbb{W},\ x\leq 4\}\\ \\ \Longrightarrow\ A=\{2x:x\in\mathbb{W},\ x<5\}$