Question

Given:

$A=\text{x : x is a multiple of 2 and is less than 25}$

$B=\text{x : x is a square of a natural number}\text{and is less than 25}$

$C=\text{x : x is a multiple of 3 and is less than 25}$

$C=\text{x : x is a prime number less than 25}$

Write the set A,B,C and D in roster form.

Answer 1

Step 1: Express set A in roster form

In roaster form method the elements of the set written inside a pair of curly braces and are Separated by commas

$\text{Given A = x : x is a multiple of 2 and is less than 25}$

The multiples of 2 and less than 25 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 and 24.

Hence, the roster form of set $\{2,4,6,8,10,12,14,16,18,20,22,24\}$

Step 2: Express set B in roster form

$\text{Given: B = x : x is a square of natural number and is less than 25}$

Squares of natural numbers less than 25 are

$1^2=1$

$2^2=4$

$3^2=9$

$4^2=16$

Hence, the roster form of set $B=\{1,4,9,16\}.$

Step 3: Express set C in roster form

$\text{Given, C= x : x is a multiple of 3 and is less than 25}$

Multiple of 3 less than 25 are 3, 6, 9, 12, 15, 18, 21 and 24.

Hence, the roster form of set $C=\{3,6,9,12,15,18,21,24\}.$

Step 4: Express set D in roster form

$\text{Given D = x : x is a prime number less than 25}$

Prime numbers less than 25 are 2, 3, 5, 7, 11, 13, 17, 19 and 23.

Hence, the roster form set $D=\{2,3,5,7,11,13,17,19,23\}.$