query: Suppose two sets of 2 elements, $\{x_1, x_2\}$ and $\{y_1, y_2\}$ are uniformly and independently chosen from the set of integers ${1, . . . , r}$
positive_passages.docid: 153168
positive_passages.text: Probability that two sets are disjoint? the same?
negative_passages.docid: 4776
negative_passages.text: Prove that the power set of an $n$-element set contains $2^n$ elements
negative_passages.docid: 146098
negative_passages.text: Number of nonempty subsets of a set with $n$ elements
negative_passages.docid: 139350
negative_passages.text: Given two coprime integers, find multiples of them that differ by 1
negative_passages.docid: 5230
negative_passages.text: Why can a 1 element set be a member of another set but not a subset of it?
negative_passages.docid: 111032
negative_passages.text: Proof of Sets involving the Cartesian Product
negative_passages.docid: 47123
negative_passages.text: Suppose that a set has an odd number of elements. Explain why half of the subsets will have an odd number of elements
negative_passages.docid: 146204
negative_passages.text: Subsets sharing at most $i$ elements
negative_passages.docid: 106756
negative_passages.text: Union and Intersection of Sets $A_{i}$ and $B_{j}$
negative_passages.docid: 147484
negative_passages.text: For a set with N members, what is the number of set partitions in which each subset is either of size 1 or 2?
negative_passages.docid: 79984
negative_passages.text: Partition of ${1, 2, ... , n}$ into subsets with equal sums.
negative_passages.docid: 85819
negative_passages.text: A non-polyhedral pair $(X,A)$ with both $X$ and $A$ polyhedral
negative_passages.docid: 121422
negative_passages.text: Independence between a constant random variable and another random variable.
negative_passages.docid: 142229
negative_passages.text: Prove that if $V \cap \text{Span}\{u_1, u_2,...,u_k\} = \{ 0\} $, then $Au_1, Au_2,...,Au_k$ are linearly independent
negative_passages.docid: 83996
negative_passages.text: For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$
negative_passages.docid: 25618
negative_passages.text: $x,y,z$ independent and uniform random on $[0,1]$, $P(x \geq  yz)$?
negative_passages.docid: 88982
negative_passages.text: Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$