using System;

using System.Linq;

using System.Collections.Generic;

​

public class ItemGroup

{

    public int ItemGroupId { get; set; }

    public int CategoryId { get; set; }

}

​

public class Item

{

    public int ItemId { get; set; }

    public List<ItemGroup> ItemGroups { get; set; }

}

​

public class Program

{   

    public static void Main(string[] args)

    {

        List<int> categories = new() { 2, 5, 7 };

        List<Item> myItems = new()

        {

            new() 

            {

                ItemId = 1,

                ItemGroups = new() 

                {

                    new() { ItemGroupId = 1, CategoryId = 1 },

                    new() { ItemGroupId = 2, CategoryId = 2 }

                }

            },

            new() 

            {

                ItemId = 2,

                ItemGroups = new() 

                {

                    new() { ItemGroupId = 3, CategoryId = 3 },

                    new() { ItemGroupId = 4, CategoryId = 4 }

                }

            },

            new() 

            {

                ItemId = 3,

                ItemGroups = new() 

                {

                    new() { ItemGroupId = 5, CategoryId = 5 },

                    new() { ItemGroupId = 6, CategoryId = 6 }

                }

            }

        };

        IEnumerable<Item> filteredItems = myItems

            .Where(i => i.ItemGroups

                .IntersectBy(categories, gr => gr.CategoryId)

                .Any());

        Console.WriteLine("ItemId of filtered items:\n");

        Console.WriteLine(string.Join(", ", filteredItems.Select(item => item.ItemId)));

    }

}

​