Question:
The number of proper subsets of a set having $n + 1$ elements is
The number of proper subsets of a set having $n + 1$ elements is
Updated On: May 12, 2024
- $2^{n +1}$
- $2^{n +1} -1 $
- $2^{n +1} -2 $
- $2^{n -2 }$
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The Correct Option is B
Solution and Explanation
If a set having n elements then its no. of subsets = $2^n$
$\therefore$ No. of proper subsets of a set having $(n + 1)$ elements = $2^{n+ 1} - 1$.
$\therefore$ No. of proper subsets of a set having $(n + 1)$ elements = $2^{n+ 1} - 1$.
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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.