query: How to prove this Tree/Set claim?
positive_passages.docid: 23008
positive_passages.text: For all $1 \leq i < j \leq k$, the subtrees $T_i$ and $T_j$ have a vertex in common. Show that $T$ has a vertex which is in all of the $T_i$.
negative_passages.docid: 3543
negative_passages.text: Prove set is basis for $R^3$
negative_passages.docid: 158882
negative_passages.text: Prove the existence of some weird family of sets
negative_passages.docid: 35115
negative_passages.text: Questions on how to prove that a set of connectives is NOT functionally complete
negative_passages.docid: 50273
negative_passages.text: How to prove $\lvert \lVert x \rVert - \lVert y \rVert \rvert \overset{\heartsuit}{\leq} \lVert x-y \rVert$?
negative_passages.docid: 42970
negative_passages.text: Proof of a proposition about recursion definition (Terence Tao's Analysis I)
negative_passages.docid: 111954
negative_passages.text: Computing the cardinality of a combinatorial set
negative_passages.docid: 72391
negative_passages.text: linear dependence proof using subsets
negative_passages.docid: 42603
negative_passages.text: How can I prove that the cadinality of a set minus a finite number of elements of it is still the same as the original set?
negative_passages.docid: 71133
negative_passages.text: prove inequlity about cardinality power sets
negative_passages.docid: 17510
negative_passages.text: Proving a set is an abelian group.
negative_passages.docid: 56370
negative_passages.text: Associative operation on a set $S$
negative_passages.docid: 99464
negative_passages.text: Proof Concerning Indexed family of Sets and Intervals
negative_passages.docid: 112084
negative_passages.text: Proof of a formula for the power set of a union of two sets
negative_passages.docid: 86263
negative_passages.text: How do we show there are the same number of elements in each of the sets?
negative_passages.docid: 77160
negative_passages.text: How to prove the cosets are distinct?
negative_passages.docid: 90590
negative_passages.text: Prove that the following set is dense