query: Is an empty set equal to another empty set?
positive_passages.docid: 26008
positive_passages.text: Why there is a unique empty set?
negative_passages.docid: 131983
negative_passages.text: Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
negative_passages.docid: 142267
negative_passages.text: If two sets have the same cardinality, then so do their power sets. Converse can't be answered?
negative_passages.docid: 3636
negative_passages.text: Are any two uncountable sets similar to each other?
negative_passages.docid: 86263
negative_passages.text: How do we show there are the same number of elements in each of the sets?
negative_passages.docid: 125077
negative_passages.text: what is the absolute value of a set?
negative_passages.docid: 107215
negative_passages.text: Is $\emptyset \in \emptyset$ or $\emptyset \subseteq \emptyset$?
negative_passages.docid: 74860
negative_passages.text: Why is the empty set a subset of every set?
negative_passages.docid: 75966
negative_passages.text: Prove that if $A$ is a set with $m$ elements, $B$ is a set with $n$ elements, and $A \cap B = \emptyset$, then $A \cup B$ has $m+n$ elements.
negative_passages.docid: 109219
negative_passages.text: How do the sets $\emptyset\times B,\ A\ \times \emptyset, \ \emptyset \times \emptyset $ look like?
negative_passages.docid: 27107
negative_passages.text: intersection of the empty set and vacuous truth
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: 126633
negative_passages.text: Is a contradiction enough to prove a set equality to $\varnothing$?
negative_passages.docid: 45508
negative_passages.text: Is the empty set a group?
negative_passages.docid: 33064
negative_passages.text: Powerset of set with empty sets
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: 39226
negative_passages.text: What's the meaning of a set to the power of another set?