How to Prove $P(A\lvert C)=P(A\lvert B^C)*P(B^C\lvert C)$
124742
P(A|C)=P(A|B)*P(B|C)?
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
124868
Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$
60761
Proof: $\cos^p (\theta) \le \cos(p\theta)$
26658
A proof for $\nabla |u|^p = p\ \text{sgn}(u)|u|^{p-1}\nabla u$.
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
51321
Prove that $A = B = C = D$
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
46746
How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
62755
The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
94119
Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$
65534
Given $P(B\mid A)=1-\varepsilon$ for some $0<\varepsilon<1$ and $P(C\mid B)=1$, prove that $P(C\mid A)≥1-\varepsilon$
107173
If $a\lt{b}$ and $c\le{d}$, prove that $a+c\lt b+d$
25258
Prove that if $ a,b,c > 0 $, then $ [(1 + a) (1 + b) (1 + c)]^{7} > 7^{7} (a^{4} b^{4} c^{4}) $.
13478
Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
43478
Prove that: $ m_a + m_b + m_c \le 4R + r $
2315
How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?