# De Morgan's Laws **A pair of laws in [[Boolean Algebra|Boolean]] and [[set algebra]] that allows for [[Disjunction|disjunctions]] and [[Union|unions]] to be expressed in terms of [[Conjunction|conjunctions]] and [[Intersection|intersections]].** > [!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]].