Question:
Write the following as intervals:
(i) {\(x: x ∈ R, -4 < x ≤ 6\)}
(ii) {\(x: x ∈ R, -12 < x < -10\)}
(iii) {\(x: x ∈ R, 0 ≤ x < 7\)}
(iv) {\(x: x ∈ R, 3 ≤ x ≤ 4\)}
Write the following as intervals:
(i) {\(x: x ∈ R, -4 < x ≤ 6\)}
(ii) {\(x: x ∈ R, -12 < x < -10\)}
(iii) {\(x: x ∈ R, 0 ≤ x < 7\)}
(iv) {\(x: x ∈ R, 3 ≤ x ≤ 4\)}
(i) {\(x: x ∈ R, -4 < x ≤ 6\)}
(ii) {\(x: x ∈ R, -12 < x < -10\)}
(iii) {\(x: x ∈ R, 0 ≤ x < 7\)}
(iv) {\(x: x ∈ R, 3 ≤ x ≤ 4\)}
Updated On: Jan 21, 2026
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Solution and Explanation
(i) {\(x: x ∈ R, -4 < x ≤ 6\)} = [-4, 6]
(ii) {\(x: x ∈ R, -12 < x < -10\)} = (-12, -10)
(iii) {\(x: x ∈ R, 0 ≤ x < 7\)} = [0, 7]
(iv) {\(x:x ∈ R, 3 ≤ x ≤ 4\)} = [3, 4]
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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.