C# Linq Check if INT exists in list of objects

I'm trying to see if an INT exists inside a list of objects. In my best attempt, below, I created a class of Person and their list of Memberships (they only contain Ids). I'm checking to see if a specific integer exists in the Person's list of Memberships.

In the code below, the Person belongs to Membership ids 1, 3, and 4. I'm trying to create a LINQ statement that when given an Integer it will return a TRUE/FALSE value if that integer exists in the Person's membership.

I created two scenarios: x = 4 should return TRUE, while x = 6 should return FALSE, but for some reason they are both returning TRUE.

What am I doing wrong?

public class Program
{
    public class Person {
      public int id {get;set;}
      public string first {get;set;}
      public string last {get;set;}     
      public List<Membership> memberships {get;set;}
    }

    public class Membership {
      public int id {get;set;}
    }   

    public static void Main()
    {

      Person p1 = new Person { id = 1, first = "Bill", last = "Jenkins"};
      List<Membership> lm1 =  new List<Membership>();
      lm1.Add(new Membership {id = 1});
      lm1.Add(new Membership { id = 3 });
      lm1.Add(new Membership { id = 4 });
      p1.memberships = lm1;

      int correct = 4;  /* This value exists in the Membership */
      int incorrect = 6;   /* This value does not exist in the Membership */

      bool x = p1.memberships.Select(a => a.id == correct).Any();
      bool y = p1.memberships.Select(a => a.id == incorrect).Any();

       Console.WriteLine(x.ToString());
            // Output:  True

       Console.WriteLine(y.ToString());
            // Output:  True     (This should be False)

    }
}