How to check if a HashSet is a subset of a collection in C#

Syntax

public bool IsSubsetOf (System.Collections.Generic.IEnumerable<T> other);

Parameters

The method takes an IEnumerable<T> collection as input.

Return value

IsSubsetOf() returns true if the HashSet is a subset of the input collection, and false otherwise.

Things to note

This method also returns true if the HashSet<T> object is empty, as an empty set is a subset of any other set, including an empty set.
IsSubsetOf() returns false if the count of elements in HashSet<T> is greater than the number of elements in the input collection.
This is an $O(n+m)$ operation, where $n$ is the count of elements in the passed collection of elements and $m$ is the number of elements in the HashSet<T>.
In special cases where the passed input collection is also a HashSet<T>, with the same equality comparer as the current HashSet<T> object, it becomes an $O(n)$ operation, where $n$ is the number of elements in the passed input collection.
The method throws an exception if the input collection is null.
The IsSubsetOf() method does not change the state of the HashSet<T>.

using System;
using System.Collections.Generic;
class HashSetSubset
{
    static void Main()
    {
        HashSet<int> numSet = new HashSet<int>();
        numSet.Add(1);
        numSet.Add(5);
        numSet.Add(9);
      
        Console.WriteLine("HashSet Elements : ");
        PrintSet(numSet);
        List<int> otherList = new List<int>{9,11,15,6,5,1};
        Console.WriteLine("Input Collection 1 : {0}", string.Join(" ", otherList.ToArray()));
        bool isSubset = numSet.IsSubsetOf(otherList);
        Console.WriteLine($"Is HashSet a subset of Input Collection 1 ?: {isSubset}");
        
        otherList = new List<int>{34,11,23,6,5,1};
        Console.WriteLine("Input Collection 2 : {0}", string.Join(" ", otherList.ToArray()));
        isSubset = numSet.IsSubsetOf(otherList);
        Console.WriteLine($"Is HashSet a subset of Input Collection 2 ? : {isSubset}");
    }
    private static void PrintSet(HashSet<int> set)
    {
      Console.Write("{");
      foreach (int i in set)
      {
          Console.Write(" {0}", i);
      }
      Console.WriteLine(" }");
    }
}

Explanation

In this code example, we create a HashSet of integers and add a few numbers to it.
We also create two lists of integers, one with all the HashSet elements and the other with a few missing elements from the HashSet.
Mathematically, a subset is a set of which all the elements are contained in another set. Therefore, the first list is a subset of the HashSet, while the second list is not.
We call IsSubsetOf() with the first list of integers as input. Since the first list has all of the elements of the HashSet, IsSubsetOf() returns true.
We call IsSubsetOf() again with the second list of integers as input. Since the second list does not have all of the elements of the HashSet, IsSubsetOf() returns false.
We also print the elements of the HashSet and both lists.