Prove that any subset of six elements of $S=\left\{1,2,...,9 \right\}$ must contain at least two elements whose sum is 10.
124667
Let $S=\{3,4,5,6,7,8,9,10,11,12\}$. Suppose 6 integers are chosen from S. Must there be 2 integers whose sum is 15?
77286
Proving set theory question
43849
Calculating number of elements commmuting with $\sigma\in S_{10}$
136306
Let $A$ be a finite set and let $B$ be a subset of $A$ with $|A|=n$,$|B|=m$ and $0<m<n$. Count the subsets of $A$ containing $ B.$
4776
Prove that the power set of an $n$-element set contains $2^n$ elements
23764
Proving that $A+A \not\subset 2A $ using a particular definition for sum of sets
114590
Prove that any finite group $G$ of even order contains an element of order $2.$
76405
Let n be an even integer. How many different ways can I choose subsets of the set {1,2...,n}
114262
Find the cardinality of the following set $S_n=\{(x,y)|x^2+y^2=n, \text{where }x,y,n \in \mathbb Z\text{ and }n\geq0 \}$
22154
Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n
75966
Prove that if $A$ is a set with $m$ elements, $B$ is a set with $n$ elements, and $A \cap B = \emptyset$, then $A \cup B$ has $m+n$ elements.
70278
$A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
64519
Subsets of a list
44214
The number of subsets of a set of cardinality $n$
81567
Pigeon hole principle to prove $a-b=9$ in subset.
134921
Find the number of all subsets of $\{1, 2, \ldots,2015\}$ with $n$ elements such that the sum of the elements in the subset is divisible by 5
3392
Sum of products of elements of nonempty subsets of A set