using System;
using System.Collections.Generic;
using System.Linq;

var first = new HashSet<int> { 1, 2 };
var second = new HashSet<int> { 1, 2 };
var third = new HashSet<int> { 1, 2, 3 };

var isEqual = first.IsSubsetOf(second) && second.IsSubsetOf(first);
//isEqual is true

var isIntersects = first.Intersect(third).Any();
//isIntersects is true

var isSubset = third.IsSubsetOf(first);
//isSubset is false

Console.WriteLine(isEqual);
Console.WriteLine(isIntersects);
Console.WriteLine(isSubset);