query: $A\subseteq B\to A\setminus B = \emptyset$. Is this true?
positive_passages.docid: 25710
positive_passages.text: $A ⊂ B$ if and only if $A − B = ∅$
negative_passages.docid: 146891
negative_passages.text: Why is $\{\emptyset\} \not = \emptyset$?
negative_passages.docid: 89712
negative_passages.text: For every set $A$, the empty set is a subset of $A$. The empty set is a set. Therefore, the empty set has a cardinality $\geq 1\ldots$
negative_passages.docid: 144502
negative_passages.text: Showing that $A\cap B = A\setminus (A\setminus B)$
negative_passages.docid: 142631
negative_passages.text: Show that A has the same cardinality as $A\setminus\{x,y,z\}$
negative_passages.docid: 28523
negative_passages.text: When would the intersection of the empty set mean anything?
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: 71653
negative_passages.text: Why is the Cartesian product of a set $A$ and empty set an empty set?
negative_passages.docid: 36631
negative_passages.text: Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
negative_passages.docid: 107234
negative_passages.text: Is the mean of equal length subsets always equal to the mean of the set?
negative_passages.docid: 36721
negative_passages.text: Is "The empty set is a subset of any set" a convention?
negative_passages.docid: 65549
negative_passages.text: What is the cartesian product of an empty set of sets?
negative_passages.docid: 16056
negative_passages.text: Is empty set element of every set if it is subset of every set?
negative_passages.docid: 136306
negative_passages.text: Let $A$ be a finite set and let $B$ be a subset of $A$ with $|A|=n$,$|B|=m$ and $0<m<n$. Count the subsets of $A$ containing $ B.$
negative_passages.docid: 120094
negative_passages.text: Prove, that for any A, B, C sets, $A\times (B\setminus C) = (A\times B)\setminus (A\times C)$ is true.
negative_passages.docid: 139841
negative_passages.text: Proving $A\setminus(B\setminus C)$ is not equal to $(A\setminus B)\setminus C$
negative_passages.docid: 56637
negative_passages.text: In naive set theory ∅ = {∅} = {{∅}}?