# De Morgan's Laws
> [!Disjunction as conjunction]
> The negation of a [[disjunction]] is the [[conjunction]] of the negations.
>
> Likewise, the complement of the [[union]] of two sets is the same as the [[intersection]] of their complements.
> $\overline{X\wedge Y}=\bar{X}\vee\bar{Y}$
> $\overline{A\cup B}=\bar{A}\cap\bar{B}$
> [!Conjunction as disjunction]
> The negation of a conjunction is the disjunction of the negations.
>
> Likewise, the complement of the intersection of two sets is the same as the union of their complements.
> $\overline{X\vee Y}=\bar{X}\wedge \bar{Y}$
> $\overline{A\cap B}=\bar{A}\cup\bar{B}$
These laws are extendable to any number of [[Boolean Function#^2dba35|literals]] and [[Set|sets]].