query: Proof of de Morgans' law: For any sets $X$ and $Y$, $\overline{X\cup Y}= \overline{X}\cap\overline{Y}$
positive_passages.docid: 143735
positive_passages.text: Prove/Disprove: For any sets $X$ and $Y$, $\overline{X\cap Y} = \bar{X}\cup\bar{Y}$
negative_passages.docid: 108704
negative_passages.text: Help with proof of $|x+y| \geq |x|-|y|$
negative_passages.docid: 127733
negative_passages.text: How to prove De Morgan’s laws without using contradictions
negative_passages.docid: 152193
negative_passages.text: The intersection of a closure with an open set
negative_passages.docid: 81671
negative_passages.text: Proof of identity $\sqrt {xy} = \sqrt x \sqrt y$ for $x,y \in \mathbb R^+$
negative_passages.docid: 13253
negative_passages.text: Prove $f(S \cup T) = f(S) \cup f(T)$
negative_passages.docid: 10477
negative_passages.text: Finding the closure of A=$\mathbb Q \cap [0,1]$.
negative_passages.docid: 103441
negative_passages.text: Proving $(A\cup B)\cap(B\cup C)\cap(C\cup A)=(A\cap B)\cup (A\cap C)\cup (B\cap C)$?
negative_passages.docid: 111122
negative_passages.text: Proof of a theorem in Hilbert's system
negative_passages.docid: 33524
negative_passages.text: Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
negative_passages.docid: 68918
negative_passages.text: Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
negative_passages.docid: 95935
negative_passages.text: Prove A = $(A \cap B) \cup (A \cap B^c)$ using the distributive and associative law.
negative_passages.docid: 32965
negative_passages.text: Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
negative_passages.docid: 27901
negative_passages.text: Proving $\sum\limits_{i=1}^k | \langle x,v_i \rangle \langle y,v_i\rangle| \leq \|x\|\cdot \|y\|$
negative_passages.docid: 80892
negative_passages.text: Does $\wp(A \cap B) = \wp(A) \cap \wp(B)$ hold? How to prove it?
negative_passages.docid: 116527
negative_passages.text: Validating a proof for necessary and sufficient conditions on sets A & B such that $P(A) \cup P(B) = P(A\cup B)$
negative_passages.docid: 35313
negative_passages.text: Proof of Euclid's Lemma