Deciding whether this is true or not. I believe the statement is true just based of the definitions of what $A \cup B$ and $A \cap B$ mean. But I'm not sure how to prove this.      For any sets A and B, if $(A \cup B)$ \ $(A \cap B ) = ∅$ , then $A = B$
This is my first post on this forum :)  I've been trying for a while to solve this problem about symmetric difference of two sets:     Given two sets $A$ and $B$, we call symmetric difference of $A$ and $B$ the following:      $$A\mathrel{\triangle}B = (A\cup B)-(A\cap B)$$      Show that if $A\mathrel{\triangle} B = \emptyset$, then $(A\subset B) \vee (B\subset A)$.   I don’t know where to start; thank you very much for the help :)
the slash (/) after a directory name on shell commands I have a little question here.  If I have two files, say filea and fileb, mv filea fileb would   delete fileb rename filea to fileb   Then if I have two directories, say dira and dirb, mv dira dirb would   move dira into dirb (it will become dirb/dira)   Noting that in both cases there are no notice or message, then this is pretty inconsistent to me. I think mv dira dirb should just overwrite dirb with the contents of dira (or merge the two directories under a directory named dirb).  I remember reading somewhere that a directory name with a slash (like dira/) is treated like a directory, and name with no slash (like dira) is treated like a file (to certain extents, of course). Anyway now I want to make the shell (zsh and possibly bash) respect my notation of a directory by using a slash. Is there a terminal option which enable me to enforce that?  To clarify, here is my desired behaviour:   mv dira dirb results in dirb being overwritten with the contents of dira mv dira dirb/ results in dira being moved into dirb (in dirb/dira)   Has anyone thought the same way as me? Or am I just weird? jQuery If DIV Doesn't Have Class "x" prevent php classes from being extends How to say that the phone is held between shoulder and ear? What are common phrases an English native speaker would use for the pose of speaking on the phone where you use your shoulder to keep the receiver against your ear (and mouth), so your hands are free?  I have some ideas, but they all sound wooden, and I don't think I've ever heard anyone describe this pose in words. It's also pretty much impossible to google for a pose or look it up on leo.org or other dictionaries.  OK, since people keep asking for what phrasings I found, I'll provide two, though I was hoping I could avoid influencing people who answer here by not providing them: "balance on one's shoulder", "held/nestled/sandwiched between shoulder and ear". Inverse metric in linearised gravity From what I've read, in the framework of linearised gravity, one perturbs the metric around a Minkowski background, $\eta_{\mu\nu}$, such that  $$g_{\mu\nu}(x)=\eta_{\mu\nu}+h_{\mu\nu}(x)\tag{1}$$  where $h_{\mu\nu}(x)$ is a small perturbation, i.e. $$\big\lvert h_{\mu\nu}\big\rvert&lt;&lt;1.\tag{2}$$  The inverse metric is then found by assuming the following ansatz:  $$g^{\mu\nu}(x)=\eta^{\mu\nu}+\tilde{h}^{\mu\nu}\tag{3}$$  where $\tilde{h}^{\mu\nu}$ is also small (i.e. $\big\lvert \tilde{h}_{\mu\nu}\big\rvert&lt;&lt;1$).   Using this, it is easy to find that  $$g^{\mu\nu}(x)=\eta^{\mu\nu}-h^{\mu\nu} \tag{4}$$  to first order.   My question is, what is the justification for this ansatz? Is it simply that one expects the inverse metric to have a similar form to the metric in order to satisfy $$g^{\mu\alpha}g_{\alpha\nu}=\delta^{\mu}_{\;\nu}~?\tag{5}$$ Highest quality website screenshot? I have created a  that i would like to add to my portfolio, but i'm having a hard time getting high quality screenshots of the full site. I tried to save the website as PDF, but that was full of errors, other online services cant recreate the images and so on. I've also just tried to take regular screenshots on the mac at put it all together, but it really lost a lot of quality when i scaled it down.  Any good ideas? :) What exactly did mv /tmp/folder/* /* do to my filesystem? It's hard to search for special characters on google, which is why I'm posting this here.  I recently ran (as root) a mv /tmp/folder/* /* when I meant to run mv /tmp/folder/* ./ Big mistake!  Things broke! A lot of files got mixed up and placed into strange places, none of the normal unix commands worked (ls, dir, cat, etc) and once you logged off, you couldn't ssh back in -- it would give you a prompt, but not accept the old passwords.  Running ls /* shows me that it performs ls on every directory in /. If I tried to draw a parallel, then mv should have simply moved (or copied?) the files to every directory in /. Instead, really weird things happened, and I was just curious what exactly was going on.  More info: The files in /tmp/folder had been transferred from a windows machine, and had been named file (#).txt, where (#) is a number up to two digits, with a space between file and the parenthesis. There were ~40 of these text files. $a+1,a-1$ invertible for nilpotent element Given a ring $R$ (with unity), prove that if $a \in R$ is nilpotent, then $a+1,a-1$ are both invertible.   Suppose $a^n=0$. Then $1=1-a^n=(1-a)(1+a+\ldots+a^{n-1})$, so $1-a$ is invertible.  If $n$ is odd we can use $1+a^n=(1+a)(1-a+\ldots+a^{n-1})$.  But what if $n$ is even? Given a compact Hausdorff space $X$, if $a \in X$ is a $G_\delta$ singleton (i.e., $\{ a \}$ is a $G_\delta$ set), then there is a countable local base at $a$.   The point $a$ can be written as countable intersection of open sets let's call $U_{n}$.  How can I use the compactness? What is the next step for proof? Could you give me hint please? Is the claim that functions of independent random variables are themselves independent, true?   I have seen that result often used implicitly in some proofs, for example in the proof of independence between the sample mean and the sample variance of a normal distribution, but I have not been able to find justification for it. It seems that some authors take it as given but I am not certain that this is always the case. Move incoming Outlook emails to folder containing previous conversation I file email conversations in various folders. But every new email in that conversation goes to inbox, so I have to manually move it to the folder that contains the rest of the conversation. Is there a way for Outlook to do this automatically with all new emails?  What I want: Outlook will do the following automatically as long as it's running:   For all unread emails in inbox... ...if email is not the first in the conversation, search for folders where that conversation is stored. If found, move the new unread email to the first* folder it finds (except for Inbox, Trash, or Sent). Optionally: If there is more than one folder containing messages in the same conversation, then do nothing.   **If there is more than one folder containing messages in the same conversation, then do nothing*. (This extra rule is not necessary if it complicates the solution too much)  Thanks! I know that packages installed with apt-get are stored in /var/cache/apt/archives.  I just installed mariadb server in Ubuntu 16.04 with following command:  sudo apt install mariadb-server   When I tried to find packages in /var/cache/apt/archives, there are no packages. Where are they stored if it's not in this directory? Why is this trigger finding a null value despite the field being populated? Where did they go?   Where do they went?   Can you please advise which of above forms is correct?  I'm pretty sure that first one is fine but wondering about second one.   Can I use a second form as well or it's incorrect? Opening PDF generated by Python AddIn using Report (*.rlf) file automatcally? As a test I have:   Authored a test.mxd with one layer called Localities in a single data frame called Layers Authored a test.rlf using View | Reports > Create Report of ArcGIS 10.2.2 for Desktop Created a Python AddIn which creates the expected PDF file from the Report (*.rlf).   This is the code which all works to create the PDF report from the Localities features within the current extent:  import arcpy  import pythonaddins  class ReportForExtent(object):     def __init__(self):         self.enabled = True         self.checked = False      def onClick(self):         mxd = arcpy.mapping.MapDocument("CURRENT")         df = arcpy.mapping.ListDataFrames(mxd,"Layers")[0]         lyr = arcpy.mapping.ListLayers(mxd,"Localities",df)[0]         arcpy.mapping.ExportReport(lyr,r"C:\temp\test.rlf",r"C:\temp\test.pdf","EXTENT",extent=df.extent)         del mxd   Is there a way to have the Python AddIn not just create the PDF file but also open it in Adobe Acrobat Reader? What is a "loop device" when mounting? How many days a year is a U.S. citizen allowed to stay in Morocco? I arrived in Morocco in October of 2014 and renewed my visa by traveling to Spain by ship for a day and getting my passport stamped again in January of 2015. My question is, am I allowed to leave the country and repeat this process this year by traveling again to another country, other than my own in order to return to Morocco for another 90 days? And if so, how many times a year is this allowed? I have read 180 days on some websites but there is not any clear answers anywhere about this that I can find. Is it possible to do a SELECT statement with a predetermined order, ie. selecting IDs 7,2,5,9 and 8 and returning them in that order, based on nothing more than the ID field?  Both these statements return them in the same order:   SELECT id FROM table WHERE id in (7,2,5,9,8)    SELECT id FROM table WHERE id in (8,2,5,9,7) In the Stack Exchange Android app, Achievements section I can see only Today's achievements. No Yesterday, Last 7 days, Last 30 days, ... details.  Previously in the 1.0.85 version itself I saw all the achievements.   I  refreshed the page many time, but still seeing Today's achievement only.  Screenshot for reference:     App Version: 1.0.85 Device Manufacturer: Motorola Device Model: XT1033 OS Version: 5.1 (2) I've start a new job today and I am trying to set up my machine to run through their Windows server.  I've managed to get a internet connection through the server now but now I can't run apt-get update as I get a "403 Forbidden" error.  This is for every repo under my source list, apart from translations(?).  I do have a proxy in apt.conf, if I don't have it I get a 407 Permission Denied error.  Here's my apt.conf file (I have omitted my username and password)  Acquire::http::proxy "http://username:password@192.168.0.2:8080/";   Here's my sources.list  #deb cdrom:[Ubuntu 12.04.2 LTS _Precise Pangolin_ - Release amd64 (20130213)]/ dists/precise/main/binary-i386/  #deb cdrom:[Ubuntu 12.04.2 LTS _Precise Pangolin_ - Release amd64 (20130213)]/ dists/precise/restricted/binary-i386/ #deb cdrom:[Ubuntu 12.04.2 LTS _Precise Pangolin_ - Release amd64 (20130213)]/ precise main restricted  # See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade to # newer versions of the distribution. deb http://gb.archive.ubuntu.com/ubuntu/ precise main restricted deb-src http://gb.archive.ubuntu.com/ubuntu/ precise main restricted  ## Major bug fix updates produced after the final release of the ## distribution. deb http://gb.archive.ubuntu.com/ubuntu/ precise-updates main restricted deb-src http://gb.archive.ubuntu.com/ubuntu/ precise-updates main restricted  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu ## team. Also, please note that software in universe WILL NOT receive any ## review or updates from the Ubuntu security team. deb http://gb.archive.ubuntu.com/ubuntu/ precise universe deb-src http://gb.archive.ubuntu.com/ubuntu/ precise universe deb http://gb.archive.ubuntu.com/ubuntu/ precise-updates universe deb-src http://gb.archive.ubuntu.com/ubuntu/ precise-updates universe  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu  ## team, and may not be under a free licence. Please satisfy yourself as to  ## your rights to use the software. Also, please note that software in  ## multiverse WILL NOT receive any review or updates from the Ubuntu ## security team. deb http://gb.archive.ubuntu.com/ubuntu/ precise multiverse deb-src http://gb.archive.ubuntu.com/ubuntu/ precise multiverse deb http://gb.archive.ubuntu.com/ubuntu/ precise-updates multiverse deb-src http://gb.archive.ubuntu.com/ubuntu/ precise-updates multiverse  ## N.B. software from this repository may not have been tested as ## extensively as that contained in the main release, although it includes ## newer versions of some applications which may provide useful features. ## Also, please note that software in backports WILL NOT receive any review ## or updates from the Ubuntu security team. deb http://gb.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse deb-src http://gb.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse  deb http://security.ubuntu.com/ubuntu precise-security main restricted deb-src http://security.ubuntu.com/ubuntu precise-security main restricted deb http://security.ubuntu.com/ubuntu precise-security universe deb-src http://security.ubuntu.com/ubuntu precise-security universe deb http://security.ubuntu.com/ubuntu precise-security multiverse deb-src http://security.ubuntu.com/ubuntu precise-security multiverse  ## Uncomment the following two lines to add software from Canonical's ## 'partner' repository. ## This software is not part of Ubuntu, but is offered by Canonical and the ## respective vendors as a service to Ubuntu users. # deb http://archive.canonical.com/ubuntu precise partner # deb-src http://archive.canonical.com/ubuntu precise partner  ## This software is not part of Ubuntu, but is offered by third-party ## developers who want to ship their latest software. deb http://extras.ubuntu.com/ubuntu precise main deb-src http://extras.ubuntu.com/ubuntu precise main   I can sort-of fix this by changing all the http in sources.list to ftp but I still have issues with ppas