internal class AccountDal
    {
        public Guid Id { get; set; }
		// more properties 
		
        public List<AccountMemberDal> Members { get; set; }
    }

	internal class AccountMemberDal
    {
        public RegisteredEntityDal Member { get; set; }
        public EAccountPermissions Permissions { get; set; } // some enum
        public bool IsAdmin { get; set; }
        public bool IsDefaultAccount { get; set; }
    }
	
	public class RegisteredEntityDal
    {
        public Guid Id { get; set; }
        public EEntityTypeDal Type { get; set; } // some enum
	}

FilterDefinition<AccountDal> filter = Builders<AccountDal>.Filter.And(
                Builders<AccountDal>.Filter.Eq(a => a.IsBusiness, true),
                Builders<AccountDal>.Filter.ElemMatch(a => a.Members, Builders<AccountMemberDal>.Filter
                .And(
                    Builders<AccountMemberDal>.Filter.Eq(a => a.IsAdmin, true),
                    Builders<AccountMemberDal>.Filter.Eq(a => a.IsDefaultAccount, false)
                    ))
                );

	ProjectionDefinition<AccountDal, AccountMemberDal> project = Builders<AccountDal>
        .Projection.ElemMatch(
                    a => a.Members, Builders<AccountMemberDal>.Filter.And(
                    Builders<AccountMemberDal>.Filter.Eq(a => a.IsAdmin, true),
                    Builders<AccountMemberDal>.Filter.Eq(a => a.IsDefaultAccount, false)
                    ));
// or
// ProjectionDefinition<AccountDal, AccountMemberDal> project = Builders<AccountDal>
// .Projection.Include(a => a.Members[-1]);
// which one is recommendes?
	
//and execute the query:
IMongoCollection<AccountDal> accounts = DbGeneralContext.Accounts;
var result = await accounts.Find(filter).Project(project).ToListAsync();

// the query that is being generated is:
db.accounts.find({ "isBusiness" : true, "members" : { "$elemMatch" : { "isAdmin" : true, "isDefaultAccount" : false } } },{ "members" : { "$elemMatch" : { "isAdmin" : true, "isDefaultAccount" : false } } })

{
        "_id" : BinData(4,"KKExCpz25hGbRAAkmxAf2Q=="),
        "members" : [
                {
                        "member" : {
                                "id" : BinData(4,"Y+gHIJv25hGbRAAkmxAf2Q=="),
                                "type" : 1
                        },
                        "permissions" : 1,
                        "isAdmin" : true,
                        "isDefaultAccount" : false
                }
        ]
}
{
        "_id" : BinData(4,"L/pKS93w5hGfMgAkmxAf2Q=="),
        "members" : [
                {
                        "member" : {
                                "id" : BinData(4,"JAUR4Hbc5hGfyQAkmxAf2Q=="),
                                "type" : 1
                        },
                        "permissions" : 1,
                        "isAdmin" : true,
                        "isDefaultAccount" : false
                }
        ]
}