Question

Write the following sets in the roster form.

(i) A = {x | x is a positive integer less than 10 and 2x – 1 is an odd number}

(ii) C = {x : x2 + 7x – 8 = 0, x ∈ R}​

Answer 1

Answer:

given the Question:-

(i) A =

(i) A ={x | x is a positive integer less than 10 and 2^(x) – 1 is an odd number}

SOLVE the equation

We given a Set-Builder form of a Set A.

A = { x | x is positive integer less than 10 and 2^x-1 is an odd }

We need to write given set in Roaster Form.

Positive integers less than 10 = 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9

Now, applying second condition we get,

we know

that 2x is always a even number.

So when 1 is subtracted from 2x

gives an odd number.

⇒ Roaster Form of

Set A = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 }

Therefore,

Set A = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 }

Answer 2

◇answer◇

(i) 2x – 1 is always an odd number for all positive integral values of x since 2x is an even number.

In particular, 2x – 1 is an odd number for x = 1, 2, … , 9.

Therefore, A = {1, 2, 3, 4, 5, 6, 7, 8, 9}

(ii) x2 + 7x – 8 = 0

(x + 8) (x – 1) = 0

x = – 8 or x = 1

Therefore, C = {– 8, 1}

HOPE IT IS HELPFUL FOR YOU