using System;
using System.Collections.Generic;

// 大文字小文字の違いを無視し、アルファベット順とは逆順にソートするためのIComparer
class CaseInsensitiveReverseStringComparer : IComparer<string> {
  public int Compare(string x, string y)
    // StringComparer.OrdinalIgnoreCase.Compareとは逆の結果を返すようにする
    => -1 * StringComparer.OrdinalIgnoreCase.Compare(x, y);
}

class Sample {
  static void Main()
  {
    var names = new[] {"Alice", "Eve", "Charlie", "Bob", "Dave"};

    var caseSensitiveSet = new SortedSet<string>(names, StringComparer.Ordinal);
    var reverseCaseInsensitiveSet = new SortedSet<string>(names, new CaseInsensitiveReverseStringComparer());

    Console.WriteLine("caseSensitiveSet");
    Console.WriteLine(string.Join(", ", caseSensitiveSet));
    Console.WriteLine(caseSensitiveSet.IsSupersetOf(new[] {"aLiCe", "BOB", "dave"}));
    Console.WriteLine();

    Console.WriteLine("reverseCaseInsensitiveSet");
    Console.WriteLine(string.Join(", ", reverseCaseInsensitiveSet));
    Console.WriteLine(reverseCaseInsensitiveSet.IsSupersetOf(new[] {"aLiCe", "BOB", "dave"}));
  }
}

caseSensitiveSet
Alice, Bob, Charlie, Dave, Eve
False

reverseCaseInsensitiveSet
Eve, Dave, Charlie, Bob, Alice
True