query: Show $xy=yx$ for all $x\in H$ and $y\in K$
positive_passages.docid: 23941
positive_passages.text: Normal Subgroups that Intersect Trivially
negative_passages.docid: 139537
negative_passages.text: Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
negative_passages.docid: 12104
negative_passages.text: How to prove this result involving the quotient maps and connectedness?
negative_passages.docid: 110075
negative_passages.text: How to show the given equality
negative_passages.docid: 142724
negative_passages.text: Prove that for all integers $x$ and $y$, $x - y$ is odd if and only if $x + y$ is odd.
negative_passages.docid: 102175
negative_passages.text: $Z=XY$, $E_Z[Z]$, $E_{X,Y}[XY]$
negative_passages.docid: 50266
negative_passages.text: In the following figure prove that: $AK||BC$
negative_passages.docid: 7775
negative_passages.text: Show that $|x-y|\leq |x|+|y|$.
negative_passages.docid: 9110
negative_passages.text: Let G be a group such that $(xy)^2 = (yx)^2$ for all x, y ∈ G. Show that $xy^2 = y^2x$ for all x, y ∈ G.
negative_passages.docid: 118727
negative_passages.text: $g(x+y)+g(x)g(y)=g(xy)+g(x)+g(y)$ for all $x,y$.
negative_passages.docid: 152311
negative_passages.text: Proving expression$\geq 2$, where variables are $x,y,z$
negative_passages.docid: 29679
negative_passages.text: Prove: $|x-y|\leq |x|+|y|$
negative_passages.docid: 116223
negative_passages.text: Show that the angles satisfy $x+y=z$
negative_passages.docid: 133880
negative_passages.text: $|\sin^2x-\sin^2y|\le K|x-y|$ find K
negative_passages.docid: 80996
negative_passages.text: A canonical construction proving $\left|HK\right| = \left|H\right|\left|K\right| / \left|H \cap K\right|$?
negative_passages.docid: 120213
negative_passages.text: Example $x$, $y$ and $z$ values for $x\uparrow^\alpha y=z$ where $\alpha\in \Bbb R-\Bbb N$
negative_passages.docid: 18313
negative_passages.text: show this inequality with $xy+yz+zx=3$