> [!NOTE] Definition (Difference) > Suppose that $X$ and $Y$ are [[Sets|sets]]. The set $X-Y=\{ x\in X \mid x \not \in Y \}$is called the difference of $X$ and $Y$ which exists by the [[Zermelo Frankel set theory (ZFC)|specification axiom]]. # Properties > [!NOTE] Lemma (Difference properties) > Suppose that $X$ is a set. Then we have the following. > (1) $X-\varnothing=X$ > (2) $\varnothing-X=\varnothing$ > (3) $X-X=\varnothing$