query: Subsets of sets containing empty set
positive_passages.docid: 858
positive_passages.text: Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$?
negative_passages.docid: 146891
negative_passages.text: Why is $\{\emptyset\} \not = \emptyset$?
negative_passages.docid: 3392
negative_passages.text: Sum of products of elements of nonempty subsets of A set
negative_passages.docid: 97951
negative_passages.text: Is the void set (∅) a proper subset of every set?
negative_passages.docid: 110485
negative_passages.text: Nested sequence of non-empty compact subsets - intersection differs from empty set
negative_passages.docid: 75935
negative_passages.text: A list containing zero elements
negative_passages.docid: 102136
negative_passages.text: How many subsets contain no consecutive elements?
negative_passages.docid: 141806
negative_passages.text: Prove that a nest of sets has an empty intersection
negative_passages.docid: 65308
negative_passages.text: Axiom of Choice: Family of non-empty sets mutually disjoint or not?
negative_passages.docid: 10229
negative_passages.text: Cyclic group generated by empty set.
negative_passages.docid: 110845
negative_passages.text: Convex Set with Empty Interior Lies in an Affine Set
negative_passages.docid: 146098
negative_passages.text: Number of nonempty subsets of a set with $n$ elements
negative_passages.docid: 3072
negative_passages.text: If the empty set is a subset of every set, why isn't $\{\emptyset,\{a\}\}=\{\{a\}\}$?
negative_passages.docid: 16056
negative_passages.text: Is empty set element of every set if it is subset of every set?
negative_passages.docid: 64519
negative_passages.text: Subsets of a list
negative_passages.docid: 71653
negative_passages.text: Why is the Cartesian product of a set $A$ and empty set an empty set?
negative_passages.docid: 110677
negative_passages.text: How is an empty set truly "empty"?