did not really help because I got confused           I found it to be *Transitive since if $A\subseteq A$ and $A\subseteq B$ then $A\subseteq B$ *Antisymmetric since $A\subseteq A$ and $A\subseteq A$ so $A=A$ *Reflective since $A\subseteq A$ and $A\subseteq A$    But I am not sure if my way of solving this or the answer is whether true or not, can anyone confirm?
Let $S$ be an arbitrary amount and define the relation $R \subseteq \mathcal{P}(S) \times \mathcal{P}(S)$ so that $(A,B) \in R$ if and only if $A \supseteq B$. Here $\mathcal{P}(S)$ is a spelling for the power set to $S$. Show that $(\mathcal{P}(S),R)$ is a partially ordered quantity.
I'm trying to make taint spread to a certain area in my world, as in, to a small NPC structure. Is there any way I can do this? I even tried using MCEdit to set the biome, but there's no "enter biome ID" thing, and Tainted Land isn't listed. Not every boolean function is constructed from $\wedge$ (and) and $\vee$ (or) Prove that not every boolean function is equal to a boolean function constructed by only using $\wedge$ and $\vee$.  Here is my solution, can I ask for a feed back on my solution please?   $p∧q$                          $0 0 0 1 $   $p∨q$  $0 1 1 1$  Not every boolean function is the same when using $ ∨ $ and $∧.$  Edited part!  $p\vee q$                  $0111$  $(p\vee q)\wedge p = p$  $0 = 0$  $0 = 0$  $1 = 1$  $1 = 1$  $(p\vee q)\vee p = p\vee q$  $0 = 0$  $1 = 1$  $1 = 1$  $1 = 1$  here is my edited answer , can I ask for more feed back , thanks Why do you write "occurred" but "listened"? The past tense of to occur is occurred (not occured), but the past tense of to listen is listened (not listenned).  Why? What is the general rule that is applied to make the past tense of a verb? Chrome 100% CPU usage, again - software_reporter_tool.exe software_reporter_tool.exe belonging to Chrome running at 100% cpu, fan full speed.  Deleting it doesn't fix anything, because it gets redownloaded again! Disabling "Protect me from bla bla" doesn't make it stop running.  Please anyone have any solutions? Example of a function such that $\varphi\left(\frac{x+y}{2}\right)\leq \frac{\varphi(x)+\varphi(y)}{2}$ but $\varphi$ is not convex I'm using Ubuntu 11.10.  The python 2.7.2 provided has a bug that has been corrected in the latest 2.7.2 sources from the python repository.  What is the recommended way to replace the ubuntu provided python with the python from source? Or put another way, how do I "update" the ubuntu-provided one?  Ideally, I would just be able to create new .deb(s) that "update" the python2.7/python2.7-dev provided by Ubuntu. Verbatim in beamer showing error: "File ended while scanning use of \@xverbatim." I am using Texmaker and MiKTeX on Windows 7. I have the following beamer code,  \documentclass{beamer} \theme{AnnArbor} \begin{document} \begin{frame} \begin{verbatim}     \begin{frame}[&lt;alignment&gt;]    \frametitle{Frame Title Goes Here}    Frame body text and/or LATEX code    \end{frame}  \end{verbatim} \end{frame} \end{document}   I was expecting the following output,         \begin{frame}[&lt;alignment&gt;]        \frametitle{Frame Title Goes Here}        Frame body text and/or LATEX code        \end{frame}   But instead I got the following Error Message,  File ended while scanning use of \@xverbatim.   Can any one please point out the error here. As far as I know verbatim can have anything inside it.  Also when I tried the following code,  \begin{verbatim}  \ begin{frame}[&lt;alignment&gt;]  \frametitle{Frame Title Goes Here}  Frame body text and/or LATEX code  \ end{frame} \end{verbatim}   I got the following output,      \ begin{frame}[&lt;alignment&gt;]      \frametitle{Frame Title Goes Here}      Frame body text and/or LATEX code     \ end{frame}   But I don't want space between \ and begin and \ and end. Apache on CentOS 5.9 VM serves modified files incorrectly If $11z^{10}+10iz^9+10iz-11 = 0$. Then possible value of $\mid z \mid,$ is If $11z^{10}+10iz^9+10iz-11 = 0$. Then possible value of $\mid z \mid,$ is  $\bf{My\; Try::}$ Given $11z^{10}+10iz^9+10iz-11 = 0\Rightarrow \displaystyle z^9 = \frac{11-10iz}{11z+10i}.$  Now Put $z = x+iy\;,$ we get $\displaystyle (x+iy)^9 = \frac{11-10i(x+iy)}{11(x+iy)+10i} = \frac{(11+10y)-10ix}{11x+i(10+11y)}$  Now i did not understand how can i solve it,  Help Required  Thanks I am using QGIS and I created a vector grid on a crop field in order to cut it into plots. I want to save each grid cell into individual polygon shapefiles automatically.  Here is an example of a vector grid I would like to split into 117 shapefiles:    Eventually, I did it manually with the selection tool and "Save as" but it is really time-consuming when there are more than 100 plots to save.    Is there any way to do it faster and more automatically?  Each plot as an attribute named "Plot" that can discriminate against them (basically being id + 1). It's the attribute used here to label them. My &quot;hat&quot; is shown twice in my answer, once in my sig, and again above. MacOS 10.14.6; Safari Version 14.0.2 (14610.3.7.1.10) Connecting two Ethernet PHY without magnetics? Proving that if $A$ is a $8\times 8$ matrix over $\mathbb{R}$ and $A^3=A$, then $A$ is diagonalizable. I need to parse  strings like "2008-09-03T20:56:35.450686Z" into Python's datetime type.  I have found  in the Python standard library, but it is not very convenient.  What is the best way to do this? Can I include another file in fstab Can I include another file in my fstab file?  I.e. can I have fstab execute lines from another file at an arbitrary point, and then return to the main file when completed? Is there a cross-browser onload event when clicking the back button? I'm trying to install Windows 8 on my pc via Microsoft Virtual PC.  However I get this annoying, non-descriptive error:    I'm looking to find out if Microsoft Virtual PC supports Windows 8, and if so how do I solve this issue?  NOTE: I'm NOT trying to ask for alternatives to Virtual PC, but rather trying to figure out if it's possible, and if so how, to use Virtual PC. Evaluate $\sum_{n=1}^\infty nx^{n-1}$ How can you evaluate $\sum_{n=1}^\infty nx^{n-1} = \frac{1}{(1-x)^2}$ without relying on the fact that it's the derivative of $\sum_{n=1}^\infty x^n = \frac{1}{1-x} $? Can I share my usb keyboard between two computers I love my Filco keyboard, I use it as primary keyboard for my Lenovo thinkpad all time. Now Im moving into the mac world and wonder:  is it possible to split my USB keyboard between two USB ports, ie one at my lenovo and one at my new iMac.   I was thinking that maybe there exists some kind of box with a switch to decide which port should receive the input, or preferable it would be possible to switch between the two via a keyboard shortcut. How to cheat and avoid cheating in Flash games?