query: Where does $(A\Delta B)\Delta C = ((A\Delta B)\cup C)\cap ((A\Delta B)^c \cup C^c)$ come from?
positive_passages.docid: 12459
positive_passages.text: Associativity of symmetric difference of sets
negative_passages.docid: 70307
negative_passages.text: $(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$
negative_passages.docid: 52135
negative_passages.text: Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
negative_passages.docid: 13167
negative_passages.text: Prove $A = (A \setminus B) \cup (A \cap B)$
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: 149553
negative_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: 118138
negative_passages.text: $\epsilon - \delta$ proof that $\lim_{x \to a} \sqrt x = \sqrt a$
negative_passages.docid: 80684
negative_passages.text: Counter example for $(A \times B) \cap (C \times D) = (A \cap C ) \times (B \cap D)$
negative_passages.docid: 57979
negative_passages.text: If $P(A \cup B \cup C) = 1$, $P(B) = 2P(A) $, $P(C) = 3P(A) $, $P(A \cap B) = P(A \cap C) = P(B \cap C) $, then $P(A) \le \frac14$
negative_passages.docid: 76823
negative_passages.text: Is it the case that for all sets $A, B, C,$ and $D$, $(A \times B) \cup (C \times D) = (A \cup B) \times (C \cup D)$?
negative_passages.docid: 144502
negative_passages.text: Showing that $A\cap B = A\setminus (A\setminus B)$
negative_passages.docid: 26302
negative_passages.text: Prove that $(X \cap Y) \cup Z = (X \cup Z) \cap (Y \cup Z)$
negative_passages.docid: 18564
negative_passages.text: Why is the symmetry variation $\delta_s q$ different from the ordinary variation $\delta q$?
negative_passages.docid: 150320
negative_passages.text: Why does $a^{b}·a^{c}=a^{b+c}$?
negative_passages.docid: 33633
negative_passages.text: Re:$ (a,b,c,d)=(pr+qs, qr-ps,pr-qs,ps+qr) $
negative_passages.docid: 138199
negative_passages.text: Proof explanation $A\setminus B = A \setminus B \cap A$
negative_passages.docid: 53610
negative_passages.text: What is the difference between $Q=\Delta U+W$ and $\Delta U=Q+W$?