query: Proving $X\setminus\bigcap_{i\in\Lambda}A_i=\bigcup_{i\in\Lambda}(X\setminus A_i)$
positive_passages.docid: 29214
positive_passages.text: Infinite DeMorgan laws
negative_passages.docid: 68918
negative_passages.text: Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
negative_passages.docid: 127720
negative_passages.text: Prove that $\bigcup_{n \in \Bbb{N}} [1/n,1] = (0,1]$.
negative_passages.docid: 152817
negative_passages.text: Proving $\sup B=\inf A$
negative_passages.docid: 98816
negative_passages.text: How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
negative_passages.docid: 13162
negative_passages.text: Prove $\alpha \in R[[x]]$ is a unit iff $a_0 \in R$ is a unit
negative_passages.docid: 64656
negative_passages.text: how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
negative_passages.docid: 75009
negative_passages.text: $A = \bigcap_{\mathfrak{p} \in \text{Spec(A)}} A_{\mathfrak{p}} = \bigcap_{\mathfrak{m} \in \text{MaxSpec(A)}} A_{\mathfrak{m}}$
negative_passages.docid: 123613
negative_passages.text: Double Complement of a set proof
negative_passages.docid: 145058
negative_passages.text: Prove $ (A \cup B) \cap C$ = $(A \cap C) \cup (B \cap C) $
negative_passages.docid: 5758
negative_passages.text: Prove that $I+\lambda A$,$I+\lambda B$,$I+\lambda C$ are invertible and A=B=C
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: 22149
negative_passages.text: How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
negative_passages.docid: 10107
negative_passages.text: Prove $A\cup (A\cap B) = A$
negative_passages.docid: 135694
negative_passages.text: Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
negative_passages.docid: 77361
negative_passages.text: How to prove $|H|[K:K \cap (g^{-1}Hg)]=|K|[H:H \cap (gKg^{-1})]$?
negative_passages.docid: 71133
negative_passages.text: prove inequlity about cardinality power sets