Please see the question which shows you two questions and two answers. Are the 2 answers contradicting each other? Can someone clarify please.    Question 1 Answer says "DOES NOT IMPLY THAT ALL X and Y...." but Question 4 answers says "IMPLIES FOR ALL X and Y
Can someone give me an example for this question on reflexivity please. How is this reflexive? Can you show an example with numbers from the set?     Question 6   Let $X = \{0,1,2,3,\dotsc, 9\}$. Define a relation $\mathcal R$ from $X$ by "$x$ is related to $y$ if $x$ and $y$ gives the same remainder on division by $3$".   (a) Show that $\mathcal R$ is an equivalence relation.   Anwser:   (a) $\mathcal R$ is clearly both reflexive and symmetric, for every number has the same (unique) remainder on division by $3$ as itself and if $a$ has the same remainder on division by $3$ as does $b$, then $b$ has the same remainder on division by $3$ as $a$ also. Similarly $\mathcal R$ is transitive, for if $a\mathcal R b$ and $b\mathcal R c$, then $a$, $b$, and $c$ all have the same remainder on division by $3$, so $a\mathcal R c$ also.
Is there a proper way to handle large combat engagements with party members involved? For instance, a party of four player characters raise a force of 30 militia men to go take a bandit camp. When they get there the bandit camp has 40 men, and none of them notable.  For the sake of simplicity, both the 30 men and the 40 bandits are armed with long swords, and wearing leather armor.   Is there a proper way to handle combat between the 30 man militia and the 40 bandits while also incorporating our four player characters? If no "proper" way exists, is there a generally accepted "best" way? Access network share from within VBScript eg FileSystemObject I've made a drush install of drupal 7.28 on my AWS server. I can confirm that the memory is set to 128M, all green on the reports -> site status page. The website will function normally and sporadically return no data, looking at the logs a tremendous amount of memory is trying to be allocated (assuming an infinite loop somewhere). Given that this is a basic install, no modules have yet been added what might be causing this?  PHP Fatal error:  Allowed memory size of 134217728 bytes exhausted (tried to allocate 140008587493184 bytes) in Unknown on line 0 VirtualBox error kernel headers I'm with Ubuntu 15.04 and I'm trying to create an emulator (genymotion), but when run virtualbox, i got the error:     Stopping VirtualBox kernel modules ...done.   Uninstalling old VirtualBox DKMS kernel modules ...done.   Trying to register the VirtualBox kernel modules using DKMSError! Your kernel headers for kernel 3.16.0-30-generic cannot be found.   Please install the linux-headers-3.16.0-30-generic package,   or use the --kernelsourcedir option to tell DKMS where it's located    ...failed!     (Failed, trying without DKMS)   Recompiling VirtualBox kernel modules ...failed!     (Look at /var/log/vbox-install.log to find out what went wrong)   I performed   uname -a   And the result is:     Linux douglas 3.16.0-30-generic #40-Ubuntu SMP Mon Jan 12 22:06:37 UTC 2015 x86_64 x86_64 x86_64 GNU/Linux   Someone help me?Already I uninstalled and installed again. Complete beginner here.  I'm trying to follow  tutorial on Anisotropic shaders, but my property panel looks nothing like the property panel in the tutorial.  For example, when creating a material, this is what his property panel looks like:    But this is what mine looks like, if I follow the same path:    I'm sure I'm missing something obvious.  How can I see the property panel shown in the tutorial? A matrix inside a table Possible Duplicate:          I am trying to insert a matrix inside a table, and I am looking for a good way to do this. Usually when I write matrices in equations, I use array environment, so I naively defined an array inside tabular, and it sort of works. The only problem is that the matrix itself seems to take up a huge amount of space inside the cell. An example is   \begin{tabular}{|c|c|} \hline \textbf{EKF} &amp; \textbf{UKF}\\ \hline $Q = \left[ \begin{array}{cc} 0.1 &amp; 0 \\ 0 &amp; 0.1 \end{array}\right]$ &amp; $Q = left[ \begin{array}{cc} 0.01 &amp; 0 \\ 0 &amp; 0.01  \end{array}\right]$\\ \hline $R = 5 \times 10^{-3}$ &amp; $R = 5 \times 10^{-5}$ \\ \hline \end{tabular}   Is there any way to increase the spacing in the cell containing the matrix without that matrix taking up all the space? What is the use of percent signs (%) at the end of lines? (Why is my macro creating extra space?) Problems with character input using scanf() I use Windows 10 with the same Microsoft account on 3 different computers, each one with a different physical keyboard layout: ITA, UK, DE.  In "Control panel - Clock and International settings - Language" I have ITA as display language with ITA/DE/UK keyboard layouts, followed by ENG(US) with only UK layout.  In the same window I opened "Advanced settings" where I set an override (second drop-down list) to the default ("the first one on the list") language/keyboard: that would be ITA/ITA, while I want (on this computer) ITA/DE.  However, when now I log in in the other computers, I get ITA/DE there as well, while each computer should have a different one, being the physical keyboards different: ITA/DE here, ITA/UK on the second one and ITA/ITA on the third one.  If I change one, they all change. And if I don't apply the override, the issue seems to be the same.  Basically the last used language AND keyboard settings are stored on the cloud and applied wherever I log in.  How to set Windows 10 to remember, PER computer, the last used language/keyboard layout settings, without having that setting follow me? How do I get whole and fractional parts from double in JSP/Java? How do I get whole and fractional parts from double in JSP/Java ? If the value is 3.25 then I want to get fractional =.25, whole = 3  How can we do this in Java? Where to set proxy ignore list? I upgraded to ubuntu 11.10 from 11.04, shocked to see few things...    My system is behind a proxy, so I did set a proxy setting. Being a web developer, I want to remove a lot of addresses that I type in browser address bar to not hit proxy. There's no such ignore list in ubuntu 11.10, what/where do I do it? What was the requirement to change the way network gui worked? How to create a hole in a polygon in QGIS? I'm trying to use the tool "delete ring" in order to create a hole in a polygon. The geometry of the hole is another feature of the same shapefile   I cannot manage to delete the part of the polygone. Does someone have a tutorial or some explanation? What is the proper usage of "not only... but also"? I'm trying to figure out how to use "not only... but also" properly. Basically, my goal is to combine two clauses by using "not only".  For negations, I've figured out two styles that both sound correct:   He knew that if he fractures his finger, not only would he not be able to compete in the water polo tournament, he would not be able to take the SAT on Monday, either. He knew that if he fractures his finger, neither would he be able to compete in the water polo tournament, nor would he be able to take the SAT on Monday.   However, I don't know how to form a sentence that does not include a negation while using "not only". Here are a few possibilities that I've considered:   Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, but he was also given a full scholarship. Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, but he was given a full scholarship. Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, he was given a full scholarship. Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, he was also given a full scholarship.   In those four possibilities, I'm varying the usage of "but" and "also" in the last clause.  What is the proper usage of "not only"? Was "book" to "beek" as "foot" is to "feet"? "Foot" is a curious word in English because it is pluralized in an unusual way; the "oo" in the word is changed to "ee".  Did this once use to be a standard way of pluralizing things in English (or a language that contributed to English), which would mean that the plural of "book" was "beek" instead of "books"?  Or, is "feet" just a one-off? Disable auto-opening nautilus window after auto-mount Every time I plug a USB stick in, nautilus opens a new window with the contents of the drive. I would like to disable this auto-opening of the nautilus window, but I would like the actual auto-mount to keep working. Is this possible? Why would var be a bad thing? Is there Ubuntu's analogue of snapshot.debian.org? Having changed the scene units and unit scale, how can I change the default size of new objects? I am using blender most of the time to model things for my 3d printer. So a default unit in "meters" is not really helpful!  Within the scene settings it is simply possible to set the units to millimeter and the unit scael to 0.001 so everything seems to work as I want it to work...   But if I add a new primitive it uses its old default sizes in meters... so a new cube get's 2000 x 2000 millimeters instead of 2x2 or whatever will be useful..  Same for all other new objects...  How can I change the default sizes of new objects permanently?   And how can I change the settings in the application templates? Right now using ctrl+u changes the "general" template - perhaps because I loaded it before...   Thanks a lot and best regards Stefan How to type \sim above another symbol x? I want to put a "~" above x, just like \hat x but replacing \hat with \sim.   How to do that? About the anime version of Air:  Some sources on the net state that Kanna's curses were broken, and her next reincarnation would be a happy one.  Some say that the pair of children playing on the beach were the reincarnations of Misuzu-Kanna / Yukito-Ryūya.  What is the canonical explanation of this ending? Did the curses really get lifted? Please include sources in your answer.