Let V be a finite set and let $\Omega \subseteq 2^{V}$ be a nested family of odd subsets of V. Show that $|\Omega| \leq \frac{3}{2}\cdot|V|$.
158507
Max family of odd subset of a nested set.
33903
Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
108995
Prove $|e^{i\theta} -1| \leq |\theta|$
134914
Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
142360
How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$
98474
Show the existence of a certain subgroup of F2
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
27889
If the set of odd numbers is a subset of $\mathbb N$ then surely it is smaller than $\mathbb N$
97583
Let $\alpha, \beta, \gamma$ be cardinals, $\beta \leq \gamma$, prove $\alpha ^{\beta}\le \alpha ^{\gamma}$
136069
Is there a simple formula for the cardinality of $\{A\subseteq\kappa\mid |A|\leq\lambda\}$ when $\lambda\leq\kappa$?
98570
Prove whether $f(n)$ is $O$, $o$, $\Omega$, $\omega$ or $\Theta$ of $g(n)$. $f(n) = n + (\log n)^{2}$, $g(n) = n + \log(n^{2})$.
10902
Showing that $ \prod\limits_{i=0}^{n} {n \choose i}\leq(\frac{2^n-2}{n-1})^{n-1} $
80180
Discrete and compact subset must be finite
66301
The cardinality of the set of countably infinite subsets of an infinite set
129813
Is there an easy proof for ${\aleph_\omega} ^ {\aleph_1} = {2}^{\aleph_1}\cdot{\aleph_\omega}^{\aleph_0}$?
122330
Prove that there exists some $c\in(-3,3)$ such that$ \ \ g(c) \cdot g''(c)<0$.
147213
Prove that finite unions of compact sets are compact