Show that $\{ x | x \in P \text{ and } x \in Q \} $ exists
37183
Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
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}$
155974
Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
5293
Show that the logic $ \ \forall x \exists y \ P(x,y) \ $ is not logically equivalent to $ \ \exists x \forall y \ P(x,y) \ $
68153
How to show that $L^p$ spaces are nested?
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
155136
$x\in \{\{\{x\}\}\}$ or not?
113892
Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
148458
$x^p-x \equiv x(x-1)(x-2)\cdots (x-(p-1))\,\pmod{\!p}$
139674
Prove $\ln\frac{p}{q}\leq \frac{p-q}{\sqrt{pq}}$ for $0<q\leq p$
153823
$|\text{rank}A-\text{rank}B|\leq \text{rank}(A+B)$
46746
How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
35236
Proof $p \vdash q \Rightarrow p$
77026
Proof with inequalities
39843
Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$