Question

List all element of the following sets

a. { 1/n ∣ n ∈ { 3 , 4 , 5 , 6 } }

b. {x∈Z ∣ x=x+1}

c. {n∈P ∣ n is a factor of 24 }

Answer 1

a) The elements are
`(1)/(3),(1)/(4),(1)/(5),(1)/(6)`

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

c) The elements are 2 and 3.

Explanation:

To find : List all element of the following sets ?

Solution :

a)
`\{(1)/(n)| n\in \{ 3 , 4 , 5 , 6 \} \}`

Here, The function is
`f(n)=(1)/(n)`

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

Substituting the values to get elements,

`f(3)=(1)/(3)`

`f(4)=(1)/(4)`

`f(5)=(1)/(5)`

`f(6)=(1)/(6)`

The elements are
`(1)/(3),(1)/(4),(1)/(5),(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.