Question:

Write the following intervals in set-builder form:
(i) (-3, 0)
(ii) [6, 12]
(iii) (6, 12]
(iv) [-23, 5)

Updated On: Oct 22, 2023
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Solution and Explanation

(i) (-3, 0) = {\(x: x ∈ R, -3 < x < 0\)}
(ii) [6, 12] = {\(x: x ∈ R, 6 ≤ x ≤ 12\)}
(iii) (6, 12] = {\(x: x ∈ R, 6 < x ≤ 12\)}
(iv) [-23, 5) = {\(x: x ∈ R, -23 ≤ x < 5\)}

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Concepts Used:

Types of Sets

Sets are of various types depending on their features. They are as follows:

  • Empty Set - It is a set that has no element in it. It is also called a null or void set and is denoted by Φ or {}.
  • Singleton Set - It is a set that contains only one element.
  • Finite Set - A set that has a finite number of elements in it.
  • Infinite Set - A set that has an infinite number of elements in it.
  • Equal Set - Sets in which elements of one set are similar to elements of another set. The sequence of elements can be any but the same elements exist in both sets.
  • Sub Set - Set X will be a subset of Y if all the elements of set X are the same as the element of set Y.
  • Power Set - It is the collection of all subsets of a set X.
  • Universal Set - A basic set that has all the elements of other sets and forms the base for all other sets.
  • Disjoint Set - If there is no common element between two sets, i.e if there is no element of Set A present in Set B and vice versa, then they are called disjoint sets.
  • Overlapping Set - It is the set of two sets that have at least one common element, called overlapping sets.