query: Are intersection of power set and power set of intersection equal?
positive_passages.docid: 155929
positive_passages.text: Let $A, B$ be sets. Show that $\mathcal P(A ∩ B) = \mathcal P(A) ∩ \mathcal P(B)$.
negative_passages.docid: 13132
negative_passages.text: If the union of two sets is contained in the intersection, then one is contained in the other ($[A\cup B\subseteq A\cap B]\implies A \subseteq B$)
negative_passages.docid: 5215
negative_passages.text: Can the principle of inclusion/exclusion be used to count elements in the intersection of a sequence of sets?
negative_passages.docid: 141806
negative_passages.text: Prove that a nest of sets has an empty intersection
negative_passages.docid: 64861
negative_passages.text: Intersection of open affines can be covered by open sets distinguished in *both*affines
negative_passages.docid: 134770
negative_passages.text: For sets $A,B$, $A \cap (B \setminus A) \subseteq \varnothing$
negative_passages.docid: 74311
negative_passages.text: Proving that the Intersection of any Collection of Compact Sets is Compact
negative_passages.docid: 87327
negative_passages.text: Unions and intersections: $(A \cup B = A ∪ C) \land (A \cap B = A ∩ C) \implies B = C.$
negative_passages.docid: 47602
negative_passages.text: Convergence of Sets? (Topology on a Powerset of a Set?)
negative_passages.docid: 37951
negative_passages.text: proof detail concerning bijection between a set and its power set
negative_passages.docid: 71358
negative_passages.text: A very interesting question: intersection point of $x^y=y^x$
negative_passages.docid: 31389
negative_passages.text: consistency of ZF\{Power Set axiom}
negative_passages.docid: 76192
negative_passages.text: Intersection of volumes defined by inequalities
negative_passages.docid: 16727
negative_passages.text: Intersection of finitely generated ideals
negative_passages.docid: 44623
negative_passages.text: Closed set as a countable intersection of open sets
negative_passages.docid: 16654
negative_passages.text: Unions and Intersections of Open Sets are Open
negative_passages.docid: 48535
negative_passages.text: Obtaining a powerset of a set in Java