Question

List all element of the following sets

Answer 1

Answer:

a) The elements are $\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6}$

b) The elements are (-∞ ...-1,0,1,2,..∞).

c) The elements are 2 and 3.

Step-by-step explanation:

To find : List all element of the following sets ?

Solution :

a) $\{\frac{1}{n}| n\in \{ 3 , 4 , 5 , 6 \} \}$

Here, The function is $f(n)=\frac{1}{n}$

Where, $n\in \{ 3 , 4 , 5 , 6 \}$

Substituting the values to get elements,

$f(3)=\frac{1}{3}$

$f(4)=\frac{1}{4}$

$f(5)=\frac{1}{5}$

$f(6)=\frac{1}{6}$

The elements are $\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6}$

b) $\{x\in \mathbb{Z} | x=x+1\}$

Here, The function is $f(x)=x+1$

Where, $x\in \mathbb{Z}$ i.e. integers (..,-2,-1,0,1,2,..)

For x=-2

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

For x=-1

$f(-1)=-1+1=0$

For x=0

$f(0)=0+1=1$

For x=1

$f(1)=1+1=2$

For x=2

$f(2)=2+1=3$

The elements are (-∞ ...-1,0,1,2,..∞).

c) $\{n\in \mathbb{P}| \text{n is a factor of 24}\}$

Here, The function is n is a factor of 24.

Where, n is a prime number

Factors of 24 are 1,2,3,4,6,8,12,24.

The prime factor are 2,3.

The elements are 2 and 3.