query: Suppose B = $B_1 \cup B_2. $ Show that $A \times B = (A \times B_1) \cup (A \times B_2)$.
positive_passages.docid: 149553
positive_passages.text: Is it always true that $(A_1 \cup A_2) \times (B_1 \cup B_2)=(A_1\times B_1) \cup (A_2 \times B_2)$
negative_passages.docid: 107383
negative_passages.text: Derived sets - prove $(A \cup B)' = A' \cup B'$
negative_passages.docid: 86505
negative_passages.text: Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$
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: 133915
negative_passages.text: In which case $M_1 \times N \cong M_2 \times N \Rightarrow M_1 \cong M_2$ is true?
negative_passages.docid: 145719
negative_passages.text: Similarity between $A$ and $B (2\times 2)$.
negative_passages.docid: 10909
negative_passages.text: $|A \cup B| = \mathfrak{c}$, then $A$ or $B$ has cardinality $\mathfrak{c}$.
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: 16749
negative_passages.text: Let $A_i= \left \{...,-2,-1,0,1,...,i \right\}$. Find $\bigcup_{i=1}^{n} A_i$ and $\bigcap_{i=1}^{n} A_i$
negative_passages.docid: 80759
negative_passages.text: Proving $A\times (B\cap C)=(A \times B)\cap (A\times C)$.
negative_passages.docid: 145058
negative_passages.text: Prove $ (A \cup B) \cap C$ = $(A \cap C) \cup (B \cap C) $
negative_passages.docid: 26861
negative_passages.text: $a+b=c \times d$ and $a\times b = c + d$
negative_passages.docid: 80876
negative_passages.text: Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
negative_passages.docid: 50159
negative_passages.text: How to prove if $\Bbb R^n=W_1\cup W_2\cup \cdots\cup $ where each $W_k$ is a subspace, then $\Bbb R^n=W_i$ holds for some $i$
negative_passages.docid: 106564
negative_passages.text: Suppose $A,B,C$ are sets. Prove that $A\mathbin\triangle B\subseteq C \iff A\cup C=B\cup C$.
negative_passages.docid: 154698
negative_passages.text: Union of Cartesian products: $X \times (Y \cup Z)= (X \times Y) \cup(X\times Z)$
negative_passages.docid: 80916
negative_passages.text: How to prove that if $A\subseteq A\times A$, then $A=\varnothing$?