query: Check the identity $A\cap (B - C)=(A\cap B) - (A\cap C)$
positive_passages.docid: 26766
positive_passages.text: Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
negative_passages.docid: 70311
negative_passages.text: Trying to prove (A ∩ B) − C = (A − C) ∩ (B − C)
negative_passages.docid: 127296
negative_passages.text: prove that a|b and b|a iff a=+-b
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: 7416
negative_passages.text: Let $ A $, $ B $ and $ C $ be sets. If $ A \cup B = A \cup C $ and $ A \cap B = A \cap C $, then show that $ B = C $.
negative_passages.docid: 111763
negative_passages.text: True or False $A - C = B - C $ if and only if $A \cup C = B \cup C$
negative_passages.docid: 143979
negative_passages.text: How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
negative_passages.docid: 13167
negative_passages.text: Prove $A = (A \setminus B) \cup (A \cap B)$
negative_passages.docid: 80876
negative_passages.text: Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
negative_passages.docid: 52973
negative_passages.text: The identity $(u\times v)\cdot(x\times y)=\begin{vmatrix}u\cdot x&v\cdot x\\ u\cdot y&v\cdot y\\\end{vmatrix}$
negative_passages.docid: 24499
negative_passages.text: Finding $(a, b, c)$ with $ab-c$, $bc-a$, and $ca-b$ being powers of $2$
negative_passages.docid: 49578
negative_passages.text: Proving $a\mathbb{Z}\cap b\mathbb{Z}=[a,b]\mathbb{Z}$
negative_passages.docid: 44484
negative_passages.text: Combinatorial identity $i{n \choose i } =n {n-1 \choose i - 1}$
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: 64656
negative_passages.text: how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
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: 90486
negative_passages.text: If $(A-B)^2=O_2$ then $\det(A^2 - B^2)=(\det(A) - \det(B))^2$