Q:

Use set-builder notation to describe the following sets: (a) {1,2,3,4,5,6,7} (b) {1, 10, 100, 1000, 10000} (c) {1,1/2, 1/3, 1/4,1/5, ...} (d) {0}

Accepted Solution

A:
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]