query: Prove $B-(B-A) = A \cap B$
positive_passages.docid: 144266
positive_passages.text: set theory proof of $A\cap B = A \setminus(A\setminus B)$
negative_passages.docid: 127293
negative_passages.text: Prove that $(a-b) \mid (a^n-b^n)$
negative_passages.docid: 90434
negative_passages.text: Prove for every two sets $A$ and $B$ that $A-B$, ${B-A}$ and $A \cap B$ are pairwise disjoint.
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: 80421
negative_passages.text: Show that $a - b \mid f(a) - f(b)$
negative_passages.docid: 5132
negative_passages.text: Given $A\cap \overline{B}\neq \emptyset$, prove $A\cup B$ connected.
negative_passages.docid: 76188
negative_passages.text: Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
negative_passages.docid: 102917
negative_passages.text: Proving statement - $(A \setminus B) \cup (A \setminus C) = B\Leftrightarrow A=B , C\cap B=\varnothing$
negative_passages.docid: 109745
negative_passages.text: If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
negative_passages.docid: 104124
negative_passages.text: Prove or disprove: $A-(B-C) = (A-B)-C$
negative_passages.docid: 111515
negative_passages.text: Proving that $-a=(-1)\cdot a$
negative_passages.docid: 123275
negative_passages.text: Prove $[A,B^n] = nB^{n-1}[A,B]$
negative_passages.docid: 80759
negative_passages.text: Proving $A\times (B\cap C)=(A \times B)\cap (A\times C)$.
negative_passages.docid: 132971
negative_passages.text: Prove that $|a| < b \iff -b<a<b$
negative_passages.docid: 14162
negative_passages.text: How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$
negative_passages.docid: 125030
negative_passages.text: Prove that $\det(A)=p_1p_2-ba={bf(a)-af(b)\over b-a}$
negative_passages.docid: 59813
negative_passages.text: Prove that for all sets A and B, A ∩ B = ∅ implies ( A ∪ B ) - B = A