Let $ \mathcal{I}$ be an ideal of $ \mathbb{N}$ i.e., if $ A\in \mathcal{I}$ and $ B\subset A$ then $ B \in \mathcal{I}$ and if $ A, B \in \mathcal{I}$ then $ A\cup B \in \mathcal{I}.$ Then if $ \mathcal{I}$ has the property that for any $ A\subset \mathbb{N}$ and $ B\subset\mathbb{N}$ either $ A\setminus B \in \mathcal{I}$ or $ B\setminus A \in \mathcal{I}$ then can anyone please suggest me that what type of ideal is this.