query: $(A=A\cup B )\Leftrightarrow B\subset A$ - is it true?
positive_passages.docid: 151852
positive_passages.text: How to prove $A \subset B \iff A \cup B = B$
negative_passages.docid: 80876
negative_passages.text: Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
negative_passages.docid: 44160
negative_passages.text: Set theory: difference between belong/contained and includes/subset?
negative_passages.docid: 134770
negative_passages.text: For sets $A,B$, $A \cap (B \setminus A) \subseteq \varnothing$
negative_passages.docid: 155063
negative_passages.text: Is Cl(f(A)) a subset of f(Cl(A))?
negative_passages.docid: 6098
negative_passages.text: Let $f:A\rightarrow B$ and $C\subset B,D\subset B$. Prove that $f^{-1}(C\backslash D)=f^{-1}(C)\backslash f^{-1}(D)$
negative_passages.docid: 64320
negative_passages.text: Prove that if $0<a<Pr(A)$ then there exists $B\subset A$ such that $Pr(B)=a$
negative_passages.docid: 13253
negative_passages.text: Prove $f(S \cup T) = f(S) \cup f(T)$
negative_passages.docid: 87327
negative_passages.text: Unions and intersections: $(A \cup B = A ∪ C) \land (A \cap B = A ∩ C) \implies B = C.$
negative_passages.docid: 127656
negative_passages.text: How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?
negative_passages.docid: 63267
negative_passages.text: Under what conditions on the sets $A$ and $B$ will it be true that $A\times B= B\times A$
negative_passages.docid: 123890
negative_passages.text: Show $A\setminus (A\cap B)=(A\cup B)\setminus B$
negative_passages.docid: 144360
negative_passages.text: For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
negative_passages.docid: 107383
negative_passages.text: Derived sets - prove $(A \cup B)' = A' \cup B'$
negative_passages.docid: 39708
negative_passages.text: Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
negative_passages.docid: 10107
negative_passages.text: Prove $A\cup (A\cap B) = A$
negative_passages.docid: 70278
negative_passages.text: $A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?