query: If $A \cap B \cap C = \varnothing$, is one $A \cap B$, $B \cap C$ or $C \cap A$ empty too?
positive_passages.docid: 142026
positive_passages.text: Show that $A∩B∩C= ∅$ is only true when $A∩B = ∅, A∩C = ∅$ or $B∩C = ∅$ or show a counterexample.
negative_passages.docid: 157218
negative_passages.text: If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$
negative_passages.docid: 130620
negative_passages.text: Identity type between A and B being non-empty implies non-emptiness of A and B?
negative_passages.docid: 52135
negative_passages.text: Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
negative_passages.docid: 21726
negative_passages.text: Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
negative_passages.docid: 124742
negative_passages.text: P(A|C)=P(A|B)*P(B|C)?
negative_passages.docid: 123498
negative_passages.text: Is "empty set" an element of a set?
negative_passages.docid: 118824
negative_passages.text: What is the complement of empty set?
negative_passages.docid: 134770
negative_passages.text: For sets $A,B$, $A \cap (B \setminus A) \subseteq \varnothing$
negative_passages.docid: 129926
negative_passages.text: Assume $A,B,C,D$ are pairwise independent events. Decide if $A\cap B$ and $B\cap D$ are independent
negative_passages.docid: 28523
negative_passages.text: When would the intersection of the empty set mean anything?
negative_passages.docid: 65549
negative_passages.text: What is the cartesian product of an empty set of sets?
negative_passages.docid: 100844
negative_passages.text: How should I understand "$A$ unless $B$"?
negative_passages.docid: 107215
negative_passages.text: Is $\emptyset \in \emptyset$ or $\emptyset \subseteq \emptyset$?
negative_passages.docid: 80199
negative_passages.text: Do we have always $f(A \cap B) = f(A) \cap f(B)$?
negative_passages.docid: 123890
negative_passages.text: Show $A\setminus (A\cap B)=(A\cup B)\setminus B$
negative_passages.docid: 102917
negative_passages.text: Proving statement - $(A \setminus B) \cup (A \setminus C) = B\Leftrightarrow A=B , C\cap B=\varnothing$