Question

Use set-builder notation to give a description of each of the following sets. Use mathematical symbols wherever possible. (a) {1,2,3,4,5} (b) {a,e,i,o,u} (c) {0,5,10,…} (d) The half-open interval [−3,5) (e) {…,−2π,−π,0,π,2π,…} (f) {1,21​,31​,41​,51​}

Answer 1

Set A can be described as... Set B can be described as... Set C can be described as... Set D can be described as... Set E can be described as... Set F can be described as...

Step-by-step explanation:

1. (a) The set {1,2,3,4,5} can be described using set-builder notation as {x : x is an element of the set of natural numbers and 1 ≤ x ≤ 5}
2. (b) The set {a,e,i,o,u} can be described using set-builder notation as {x : x is a vowel in the English alphabet}
3. (c) The set {0,5,10,...} can be described using set-builder notation as {x : x is an element of the set of whole numbers and x ≤ 10 and x is a multiple of 5}
4. (d) The set [-3,5) can be described using set-builder notation as {x: -3 ≤ x < 5}
5. (e) The set {...,-2π,-π,0,π,2π,...} can be described using set-builder notation as {x : x is an element of the set of real numbers and x is a multiple of π}
6. (f) The set {1,21⁄,31⁄,41⁄,51⁄} can be described using set-builder notation as {x : x is an element of the set of rational numbers and x = (10x + 1)/10}