Probability Proof $ \mathbb{P}\left(A_{1} \cup A_{2} \cup A_{3}\right) = ... $
121457
Probability of a Union
110876
Prove that $p\mid \binom{p}{k},\ 0< k< p$
27899
Can we prove the existence of $A\cup B$ without the union axiom?
122326
Proving $|P(A\cap B)-P(A)P(B)|\leq \frac{1}4$
90283
Proof that $3 \mid \left( a^2+b^2 \right)$ iff $3 \mid \gcd \left( a,b\right)$
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
50202
Probablity identities and $A$ given $B$
21097
If $A$ and $B$ are independent events, and $A$ and $C$ are independent events, how do I show that $A$ and $B\cup C$ are independent?
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
145884
Showing $\left|\frac{a+b}{2}\right|^p+\left|\frac{a-b}{2}\right|^p\leq\frac{1}{2}|a|^p+\frac{1}{2}|b|^p$
18714
$\gcd\left(a+b,\frac{a^p+b^p}{a+b}\right)=1$, or $p$
78356
How to prove ${n \choose p} \equiv\left\lfloor \frac{n}{p} \right\rfloor\pmod p$
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
85287
Prove that, for $p > 3$, $(\frac 3p) = 1$ when $p \equiv 1,11 \pmod{12}$ and $(\frac 3p) = -1$ when $p \equiv 5,7 \pmod{12}$
138962
$X$ is a random variable, if $\Bbb E(X^2)=1$ and $\Bbb E(X)\geq a>0$, prove that $\Bbb P(X\geq\lambda a)\geq(a-\lambda a)^2$ for $0\leq\lambda\leq 1$.
139537
Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
76635
Proof through combinatorial argument