Prove that: $P(A) \bigcap P(B) = P(A\bigcap B)$
36789
The power set of the intersection of two sets equals the intersection of the power sets of each set
26833
Prove that $\mathbb P(X>Y) =\frac{b}{a + b}$ if $X, Y$ are exponentially distributed with parameters $a$ and $b$.
43219
If $[K(\alpha):K]=p\neq q=[K(\beta):K]$ then $[K(\alpha+\beta):K]=pq$
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
68781
proving if $a \le b$ then $\sup(A) \le \inf(B)$
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
95800
Prove that if $\mathcal P(A) \cup \mathcal P(B)= \mathcal P(A\cup B)$ then either $A \subseteq B$ or $B \subseteq A$.
3273
Trouble in proving that $\|x\|_p = \max|x_j|$
67394
How to interpret $\mathbb{P}(B|A)$ when $\mathbb{P}(A) = 0$
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
144502
Showing that $A\cap B = A\setminus (A\setminus B)$
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
60707
Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
147888
Show that $M=\bigcap_{\mathfrak{p}\in\operatorname{Spec}(R)}M_\mathfrak{p}=\bigcap_{\mathfrak{m}\in\text{Max}(R)}M_\mathfrak{m}$ for certain $M$.
13026
Prove that if AB=I_m, then rk(A)=rk(B).