Show that $A[x] \cap A[x^{-1}]$ is integral over $A$.
7903
Prove that $B[x] \cap B[x^{-1}]$ is integral over $B$
49578
Proving $a\mathbb{Z}\cap b\mathbb{Z}=[a,b]\mathbb{Z}$
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
80876
Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
20415
Show that the integral of a positive function is positive
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
75863
how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$
131120
Proving an integral equation.
37398
Proof that$ (a+A)\cap A=\varnothing$ if $A$ is countable
133406
$n^a$ integral for all integer $n$ implies $a$ integral
13174
Show that $A[X]/(aX+b)$ is an integral domain
64932
Show that $\lim_{x\to a^{+}} g(x) =g(a)$
10107
Prove $A\cup (A\cap B) = A$
15312
Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
136966
Riemann integral proof $\int^b_a f(x) \, dx>0$
110643
What are the strategies I can use to prove $f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(T)$?