Respuesta :
Answer:
a) The elements are [tex]\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6}[/tex]
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) [tex]\{\frac{1}{n}| n\in \{ 3 , 4 , 5 , 6 \} \}[/tex]
Here, The function is [tex]f(n)=\frac{1}{n}[/tex]
Where, [tex]n\in \{ 3 , 4 , 5 , 6 \}[/tex]
Substituting the values to get elements,
[tex]f(3)=\frac{1}{3}[/tex]
[tex]f(4)=\frac{1}{4}[/tex]
[tex]f(5)=\frac{1}{5}[/tex]
[tex]f(6)=\frac{1}{6}[/tex]
The elements are [tex]\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6}[/tex]
b) [tex]\{x\in \mathbb{Z} | x=x+1\}[/tex]
Here, The function is [tex]f(x)=x+1[/tex]
Where, [tex]x\in \mathbb{Z}[/tex] i.e. integers (..,-2,-1,0,1,2,..)
For x=-2
[tex]f(-2)=-2+1=-1[/tex]
For x=-1
[tex]f(-1)=-1+1=0[/tex]
For x=0
[tex]f(0)=0+1=1[/tex]
For x=1
[tex]f(1)=1+1=2[/tex]
For x=2
[tex]f(2)=2+1=3[/tex]
The elements are (-∞ ...-1,0,1,2,..∞).
c) [tex]\{n\in \mathbb{P}| \text{n is a factor of 24}\}[/tex]
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.
