query: proving cartesian product is distributive over unions and intersections
positive_passages.docid: 25553
positive_passages.text: elementary set theory (cartesian product and symmetric difference proof)
negative_passages.docid: 41783
negative_passages.text: Cardinality of the Cartesian Product of Two Equinumerous Infinite Sets
negative_passages.docid: 146664
negative_passages.text: The union of two linearly independent subsets
negative_passages.docid: 16654
negative_passages.text: Unions and Intersections of Open Sets are Open
negative_passages.docid: 59273
negative_passages.text: Cartesian product of embeddings is embedding
negative_passages.docid: 91777
negative_passages.text: Product of Non-Disjoint Cycles
negative_passages.docid: 62687
negative_passages.text: Proving Cardinality of Cosets in Abstract Algebra
negative_passages.docid: 29303
negative_passages.text: Cartesian product of compact sets is compact
negative_passages.docid: 34768
negative_passages.text: Proving $(p \oplus q) \oplus r=p \oplus (q \oplus r)$
negative_passages.docid: 9651
negative_passages.text: Cardinality of cartesian product of an infinite set with N
negative_passages.docid: 109070
negative_passages.text: Question about the proof of the distributive property for sets
negative_passages.docid: 103106
negative_passages.text: Proving that any permutation in $S_n$ can be written as a product of disjoint cycles
negative_passages.docid: 118560
negative_passages.text: Ordered N-Tuples as Cartesian Products of Indexed Families
negative_passages.docid: 1627
negative_passages.text: Cartesian product of an arbitrary number of sets
negative_passages.docid: 32772
negative_passages.text: Proving units in a ring
negative_passages.docid: 42141
negative_passages.text: Proving Distributivity of Matrix Multiplication
negative_passages.docid: 84437
negative_passages.text: Prove that the projection $p_i$ from the product space $X_I S_i \tau$ into $S_i \tau_i$ is open for each $i \in I$