Answer:
A) The set builder notation is: {n | n∈Z, 1≤n≤7}.
B) The set builder notation is: ![\{10^x | x=0,1,2,3,4\}](https://tex.z-dn.net/?f=%5C%7B10%5Ex%20%7C%20x%3D0%2C1%2C2%2C3%2C4%5C%7D)
C) The set builder notation is: ![\{\frac{1}{n} | n\in z\}](https://tex.z-dn.net/?f=%5C%7B%5Cfrac%7B1%7D%7Bn%7D%20%7C%20n%5Cin%20z%5C%7D)
D) The set builder notation can be: ![\{x\ \in R | x=x^3\ and\ x\neq 1\}](https://tex.z-dn.net/?f=%5C%7Bx%5C%20%5Cin%20R%20%7C%20x%3Dx%5E3%5C%20and%5C%20x%5Cneq%201%5C%7D)
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:
![\{1, 10, 100, 1000, 10000\}=\{10^0, 10^1, 10^2, 10^3, 10^4\}](https://tex.z-dn.net/?f=%5C%7B1%2C%2010%2C%20100%2C%201000%2C%2010000%5C%7D%3D%5C%7B10%5E0%2C%2010%5E1%2C%2010%5E2%2C%2010%5E3%2C%2010%5E4%5C%7D)
Thus, the set builder notation is: ![\{10^x | x=0,1,2,3,4\}](https://tex.z-dn.net/?f=%5C%7B10%5Ex%20%7C%20x%3D0%2C1%2C2%2C3%2C4%5C%7D)
(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: ![\{\frac{1}{n} | n\in z\}](https://tex.z-dn.net/?f=%5C%7B%5Cfrac%7B1%7D%7Bn%7D%20%7C%20n%5Cin%20z%5C%7D)
(d) {0}
The set builder notation can be: ![\{x\ \in R | x=x^3\ and\ x\neq 1\}](https://tex.z-dn.net/?f=%5C%7Bx%5C%20%5Cin%20R%20%7C%20x%3Dx%5E3%5C%20and%5C%20x%5Cneq%201%5C%7D)