Answer:
A) The set builder notation is: {n | n∈Z, 1≤n≤7}.
B) The set builder notation is: [tex]\{10^x | x=0,1,2,3,4\}[/tex]
C) The set builder notation is: [tex]\{\frac{1}{n} | n\in z\}[/tex]
D) The set builder notation can be: [tex]\{x\ \in R | x=x^3\ and\ x\neq 1\}[/tex]
Step-by-step explanation:
Consider the provided information,
We need to use set-builder notation to describe the following sets.
(a) {1,2,3,4,5,6,7}
Here, the number are integer starting from 1 to 7.
Thus, the set builder notation is: {n | n∈Z, 1≤n≤7}.
(b) {1, 10, 100, 1000, 10000}
The above set can be written as:
[tex]\{1, 10, 100, 1000, 10000\}=\{10^0, 10^1, 10^2, 10^3, 10^4\}[/tex]
Thus, the set builder notation is: [tex]\{10^x | x=0,1,2,3,4\}[/tex]
(c) {1, 1/2, 1/3, 1/4, 1/5, ...}
Here the numerator is 1 for each term but denominator is natural number.
Thus, the set builder notation is: [tex]\{\frac{1}{n} | n\in z\}[/tex]
(d) {0}
The set builder notation can be: [tex]\{x\ \in R | x=x^3\ and\ x\neq 1\}[/tex]
