Finding nil has_one associations in where query

Question

This may be a simple question, but I seem to be pulling my hair out to find an elegant solution here. I have two ActiveRecord model classes, with a has_one and belongs_to as

Answer 1

Found two other railsey ways of doing this:

Item.includes(:purchase).references(:purchase).where("purchases.id IS NULL")

Item.includes(:purchase).where(purchases: { id: nil })

Technically the first example works without the 'references' clause but Rails 4 spits deprecation warnings without it.