Question:
Write down all the subsets of the following sets:
(i) {a}
(ii) {a, b}
(iii) {1, 2, 3}
(iv) \(\phi\)
Write down all the subsets of the following sets:
(i) {a}
(ii) {a, b}
(iii) {1, 2, 3}
(iv) \(\phi\)
(i) {a}
(ii) {a, b}
(iii) {1, 2, 3}
(iv) \(\phi\)
Updated On: Oct 22, 2023
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Solution and Explanation
(i) The subsets of {a} are \(\phi\) and {a}.
(ii) The subsets of {a, b} are \(\phi\), {a}, {b}, and {a, b}.
(iii) The subsets of {1, 2, 3} are \(\phi\), {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, and {1, 2, 3}
(iv) The only subset of \(\phi\) is \(\phi\).
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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.