List all element of the following setsa. { 1/n ∣ n ∈ { 3 , 4 , 5 , 6 } }b. {x∈Z ∣ x=x+1}c. {n∈P ∣ n is a factor of 24 }
Accepted Solution
A:
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 numberFactors of 24 are 1,2,3,4,6,8,12,24.The prime factor are 2,3.The elements are 2 and 3.