Question:

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 = $2^{n+ 1} - 1$.
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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.