Question

Write the roster form of {X:X is +integer less than 10 and 2x-1 is odd no.}

Answer 1

Our set in set builder form is given by,

$\{x:x\ \text{is a positive integer less than 10 and 2x-1 is an odd number}\}$

Well, for every integers  $x,$  not only for some positive integers less than 10,  it is always true that  $2x-1$  is an odd integer.

Because it leaves remainder 1 on division by 2,

$2x-1=2x-2+1=2(x-1)+1$

So every integers which are not exactly divisible by 2 are said to be odd integers, no need to be doubted!

Then why it's mentioned in set builder notation that  $\text{ 2x-1 is an odd number}\ ?$

It's just for confusing, I guess! So, ignore it!

Thus our set in set builder form is simplified as,

$\{x:x\ \text{is a positive integer less than 10}\}$

Hence, our set in roster form is simply got!

$\Large\{1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9\}$