query: A∩B∩C=∅, then A∩B=∅,A∩C=∅ or B∩C=∅
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: 139018
negative_passages.text: A does the same B as does C
negative_passages.docid: 83996
negative_passages.text: For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$
negative_passages.docid: 28523
negative_passages.text: When would the intersection of the empty set mean anything?
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: 107215
negative_passages.text: Is $\emptyset \in \emptyset$ or $\emptyset \subseteq \emptyset$?
negative_passages.docid: 142993
negative_passages.text: Proof of A ⊆ C and B ⊆ C ⇔ A ∪ B ⊆ C
negative_passages.docid: 118239
negative_passages.text: If $A, B, C$ are sets prove that $(A\setminus B)\setminus C\subseteq A\setminus(B\setminus C)$
negative_passages.docid: 123890
negative_passages.text: Show $A\setminus (A\cap B)=(A\cup B)\setminus B$
negative_passages.docid: 150825
negative_passages.text: Is an empty set equal to another empty set?
negative_passages.docid: 114599
negative_passages.text: $A \cup B$ and $A \cap B$ connected $\implies A$ and $B$ are connected
negative_passages.docid: 131983
negative_passages.text: Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
negative_passages.docid: 70307
negative_passages.text: $(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$
negative_passages.docid: 74077
negative_passages.text: A intersection (A union B)
negative_passages.docid: 113377
negative_passages.text: Empty preimage of an intersection implies empty intersection of the preimages
negative_passages.docid: 124742
negative_passages.text: P(A|C)=P(A|B)*P(B|C)?
negative_passages.docid: 87928
negative_passages.text: Proof of logical equivalence of biconditional and other proposition