Объединение

using System;
using System.Collections.Generic;

namespace array
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] stringSet1 = { "1", "2", "1" };
            string[] stringSet2 = { "4", "3", "2" };
            List<string> combinedCollection = new List<string>();

            AddSingleRecords(stringSet1, combinedCollection);
            AddSingleRecords(stringSet2, combinedCollection);
            ShowList(combinedCollection);
        }

        private static void AddSingleRecords(string[] stringSet, List<string> singlesList)
        {
            foreach (string element in stringSet)
                if (singlesList.Contains(element) == false)
                    singlesList.Add(element);
        }

        private static void ShowList(List<string> collection)
        {
            foreach (string element in collection)
                Console.Write($"{element} ");
        }
    }
}