Prove that for all $a \in N$ and $b \in K, aba^{−1}b ^{−1} \in N \bigcap K.$
106779
How to show if $H,K$ are normal subgroups in a group $G$ then $[H,K] \leq H \cap K$
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
42292
Show that $a_n<\sqrt{2}$ for every $n\in\mathbb{N}$.
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
147253
Prove for any $K \leq G$, either $K \leq N$ or $KN=G$ and $[K:K \cap N]=p$ where N is normal in G and $[G:N]=p$
80009
Prove that $| |a|-|b| | \le |a-b|$
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
128710
Prove that $\langle a^n \rangle \bigcap \langle a^k \rangle = \langle a^{lcm (n,k)} \rangle$
32155
Prove that if for every $x \in \mathbb{R}^N$ $Ax=Bx$ then $A=B$
151544
Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$
122326
Proving $|P(A\cap B)-P(A)P(B)|\leq \frac{1}4$
88995
Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$.
140446
Prove that $A \smallsetminus (A \smallsetminus B) = A \cap B$
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$