query: (A−B)∪(B−A)=(A∪B) − (A∩B)
positive_passages.docid: 26592
positive_passages.text: The symmetric Difference
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: 104124
negative_passages.text: Prove or disprove: $A-(B-C) = (A-B)-C$
negative_passages.docid: 95935
negative_passages.text: Prove A = $(A \cap B) \cup (A \cap B^c)$ using the distributive and associative law.
negative_passages.docid: 142026
negative_passages.text: Show that $A∩B∩C= ∅$ is only true when $A∩B = ∅, A∩C = ∅$ or $B∩C = ∅$ or show a counterexample.
negative_passages.docid: 70311
negative_passages.text: Trying to prove (A ∩ B) − C = (A − C) ∩ (B − C)
negative_passages.docid: 43310
negative_passages.text: Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
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: 143979
negative_passages.text: How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
negative_passages.docid: 38200
negative_passages.text: Show that $(\mathbf{a}·\mathbf{a})(\mathbf{b}·\mathbf{b})-(\mathbf{a}·\mathbf{b})^2=(\mathbf{a}\times\mathbf{b})·(\mathbf{a}\times\mathbf{b})$?
negative_passages.docid: 13136
negative_passages.text: Element chasing proof that $(A\setminus C)\setminus(B\setminus C) = (A\setminus B)\setminus C$
negative_passages.docid: 113211
negative_passages.text: Arithmetics of cardinalities: if $|A|=|C|$ and $|B|=|D|$ then $|A\times B|=|D\times C|$
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: 68918
negative_passages.text: Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
negative_passages.docid: 91829
negative_passages.text: Prove $(ah,bk)=(a,b)(h,k)\left(\frac{a}{(a,b)},\frac{k}{(h,k)}\right)\left(\frac{b}{(a,b)},\frac{h}{(h,k)}\right)$
negative_passages.docid: 24856
negative_passages.text: Proving sup(A + B) = sup A + sup B
negative_passages.docid: 5149
negative_passages.text: Show $\binom{a}{b}\binom{b}{c}=\binom{a}{a-c}\binom{a-c}{a-b}$