query: How to show $A\times (B\cup C) = (A\times B)\cup (A\times C)$
positive_passages.docid: 154698
positive_passages.text: Union of Cartesian products: $X \times (Y \cup Z)= (X \times Y) \cup(X\times Z)$
negative_passages.docid: 83713
negative_passages.text: If $z,w\in \mathbb{C}^{\times}$, then $|z+w|=|z|+|w|$ iff $w=tz$ for some $t\gt 0$
negative_passages.docid: 61103
negative_passages.text: Prove that $\mathbb{|Q| = |Q\times Q|}$
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: 125008
negative_passages.text: Define a bijection between $Z^{X \cup Y}$ and $Z^X \times Z^Y$, where $X, Y \in \mathcal{P}(\Omega) $ and $X \cap Y = \emptyset$
negative_passages.docid: 144502
negative_passages.text: Showing that $A\cap B = A\setminus (A\setminus B)$
negative_passages.docid: 75604
negative_passages.text: Proof that $\partial(A\times B) = ((\partial A)\times B)\cup (A\times(\partial B))$
negative_passages.docid: 38428
negative_passages.text: How tot start proving $A \times B \times C \ne (A \times B) \times C$?
negative_passages.docid: 38507
negative_passages.text: Show that $\mathbb{Q}\times \mathbb{Q}$ is denumerable
negative_passages.docid: 120642
negative_passages.text: Let $g : \Bbb N \times \Bbb N \to\Bbb N \times \Bbb N$ defined as $g(m,n) = (m + n,m - n)$
negative_passages.docid: 53327
negative_passages.text: $C_2 \times C_2$ and $C_4$
negative_passages.docid: 5149
negative_passages.text: Show $\binom{a}{b}\binom{b}{c}=\binom{a}{a-c}\binom{a-c}{a-b}$
negative_passages.docid: 77902
negative_passages.text: If $A,B,$ and $C$ are sets, then $A\times(B-C)$ = $(A \times B)$ $-$ $(A \times C)$.
negative_passages.docid: 6161
negative_passages.text: The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
negative_passages.docid: 68258
negative_passages.text: Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$
negative_passages.docid: 80876
negative_passages.text: Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
negative_passages.docid: 47434
negative_passages.text: Proof that $A \subseteq B \Leftrightarrow A \cup B = B$