query: Let $a$,$b\in \mathbb{Z}$, not both zero. Prove set $S$
positive_passages.docid: 74631
positive_passages.text: For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $
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: 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: 77286
negative_passages.text: Proving set theory question
negative_passages.docid: 50939
negative_passages.text: If $A$ and $B$ are nonempty sets, prove that $A \times B = B \times A$ if and only if $A = B$
negative_passages.docid: 110256
negative_passages.text: Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
negative_passages.docid: 13167
negative_passages.text: Prove $A = (A \setminus B) \cup (A \cap B)$
negative_passages.docid: 39114
negative_passages.text: Prove that a set in $\mathbb R^3$ is not an algebraic set
negative_passages.docid: 17510
negative_passages.text: Proving a set is an abelian group.
negative_passages.docid: 46240
negative_passages.text: Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
negative_passages.docid: 123467
negative_passages.text: Prove that $f(z) = e^z$ maps $\mathbb{C} \setminus B $ onto $\mathbb{C} \setminus \{0\}$.
negative_passages.docid: 144266
negative_passages.text: set theory proof of $A\cap B = A \setminus(A\setminus B)$
negative_passages.docid: 151544
negative_passages.text: Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$
negative_passages.docid: 137707
negative_passages.text: How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
negative_passages.docid: 40162
negative_passages.text: Prove that the set $\mathbb{Q}[\alpha] = \{a+b\alpha+c\alpha^2 \mid a, b, c \in\mathbb{Q}\}$ is closed under addition and multiplication.
negative_passages.docid: 143067
negative_passages.text: Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.
negative_passages.docid: 59134
negative_passages.text: Proving idempotent elements in $\mathbb{Z}_n$