Working on P.D. Magnus. forallX: an Introduction to Formal Logic (pp. 154, exercise D. 7). It is the last exercise of Chapter 16. This is what I got so far.   Is my $IP$ strategy correct ?  $\def\fitch#1#2{\quad\begin{array}{|l}#1\\\hline#2\end{array}} \fitch{}{  \fitch{¬(((A \to B) \to B) \to B)}{    \fitch{¬((A \to B) \to B) }{      \fitch{¬(A \to B)}{        \fitch{B}{          \fitch{A}{            B           } \\           A \to B \\           \bot         }       }     }   } }$  P.S: Here is a link to the open-source book:
Using the Fitch system, how do I prove $((p \implies q) \implies p)\implies p$? I started with the hypotheses $(p \implies q) \implies p$ and $\sim p$. However, from these hypotheses I did not get the desired contradiction to solve the question.  Thanks sb45
My wireless/WiFi connection does not work. What information is needed to diagnose the issue? Your situation   You have successfully installed Ubuntu.  You have just downloaded and booted Ubuntu live media.  The latest LTS (see also ) or latest non-LTS release are preferred. See the list of  that are currently supported.) You upgraded your Ubuntu installation to the latest release that the software updater offered you. WiFi worked before, but not now on the new release. You  to new hardware.   Your problem   The wireless of your laptop or desktop is not working. You tried switching the wireless switch off and on and you tried rebooting several times, but you don't see any WiFi access points. You can see your wireless access point, but you cannot establish a connection. You want to analyze the problem, but you don't know where to start or what information you can provide.   This question and answer was written to give people the wireless script that will provide the information needed in most cases to diagnose their wireless issue's.   Related questions I'm working through some old integrals and I found one that's interesting. I can't quite remember how it's proved, so if someone could set me off in the right direction, it would be really helpful. Thanks!   $\int_{\mathbb{R}} e^{-ax^2 + bx} dx = \sqrt{ \dfrac{\pi}{a}} e^{\frac{b^2}{4a}}$  I've tried change of variable, but I'm not sure this is the right approach. I built a model of multiple linear regression to predict the revenues at the box office of a movie: the variable $Y$ is revenue while the variables $X$ are two: Activity (number of tweets per day) and sentiment (connotation of these tweets).  The problem is that the intercept is not significant. I thought of a possible explanation: the intercept in practice is the value of the variable $Y$ when the variables $X$ assume values of 0; but because of the very strong development of social networks, it is virtually impossible not to have even a tweet (and then a wave of activity) about a movie that just came out, I thought that the significance or not the intercept could be neglected because the assumed value has no meaning in reality (a tweet of 0 would never be satisfied, given the market today). In this way, I consider the intercept a mere constant for the calculation of the line, without worrying about its significance (because in some cases would take negative values, which is impossible for revenues).  The interpretation may be correct? What documentation is needed for a tourist to drive a US citizen's car? Using Apple Script to Manage Sound Output Selection I am brand new here and I have an additional clarification or need additional help for an issue from this thread -   In my preference pane, in addition to Headphones and Digital out, I also have 2 apple monitors and would like the option of selecting one of them as out put (namely the first one in the list).   Basically I need help with adjust his solution to be able to select the third row or first monitor as sound output.  Or a way to accomplish this without knowing how to edit AppleScript for a different setup. Capture characters from standard input without waiting for enter to be pressed How to change keyboard layout in Lubuntu 15.10? I have recently upgraded my PC from Lubuntu 14.10 to 15.10. Before the upgrade my keyboard layout matched my Danish keyboard. But after the upgrade I probably have a standard English/US layout.   Preferences/Language Support, doesn't let me configure the keyboard layout. Preferences/Keyboard and Mouse, only let me configure stroking delay and similar.    I don't know about iBus and fcitx, as far as the tooltip infomation tells me, its for more complex languages such as Chinese.  I don't have a US icon in the taskbar, no keyboard and/or language icon at all.  Things I have tried:   Running the following in a terminal works, but only until the next reboot:  setxkbmap -layout dk  I got the following parameter in the file /etc/default/keyboard:  XKBLAYOUT="dk"  Installing and running the app Lxkeymap changes the keyboard to Danish when I run it, but rebooting will change the layout back to US.   I don't want anything fancy, I just want to set my keyboard layout to Danish. How can I do that? I got a integrated GD, which is Intel, and another discrete GD, AMD Radeon 6490 HD I am using ubuntu 11.10  1st, when I boot into Windows, my GD is indeed AMD Radeon 6490 HD, but when I boot into Ubuntu, it shows that I have AMD Radeon 6470 instead.  2nd, I try most methods only to install driver for my AMD/ATI graphic card. First by jockey(fail, boot with unity 2D instead) and install manually (fail, boot into blank screen).   3rd, I give up using the AMD/ATI graphic card. Then I got a new problem. Both my graphic cards are powered on on startup, which causes my laptop to over heat.   I view the content of /sys/kernel/debug/vgaswitcheroo/switch  0:DIS: :Pwr:0000:01:00.0 1:IGD:+:Pwr:0000:00:02.0   Then I switch off IGD using echo OFF &gt; /sys/kernel/debug/vgaswitcheroo/switch and I get  0:DIS: :Off:0000:01:00.0 1:IGD:+:Pwr:0000:00:02.0   But after I reboot, the discrete graphic card is powered on again. How to solve this? Simulation software to solve high school level mechanics problems I'm a physics teacher and I would like to find a simulation software that could be used to give exact numerical answers to high school level problems in Newtonian mechanics.  I want the students to first calcultate a numerical answer to a physics problem and then use the simulator to visualize the problem in order to understand it better and verify that the simlator gives the same answer that they got when doing the calculation themselves.  Here are some examples of what kind of problems I want the students to be able to solve with the simulator:   A slope with a specific angle of inclination and a ball starts rolling at a certain point. Determine the speed, angular momentum and total mechanical energy of the ball after a specific time t. A ladder of known mass and length is leaning against the wall at a specific angle. The contact between the ladder and the wall is frictionless. Calcultate the x and y components of the force between the floor and the ladder.   I would like the software to have the following features:  - Simulation in 2D. No 3D simulations are necessary and the software should at least have the option of doing simulations only in 2D.  - Position all objects exactly by writing numbers (just positioning the objects using the mouse is not precise enough).  - Show animations of the time evolution of the system.  - Show forces, velocities and accelerations as arrows.  - Give exact numerical results so that the students can use the software to verify their calculation.  Ideally the software would have a graphical user interface, but if no suitable software with graphical interface exixts, I could also consider a software with text-based inputs. I would consider both free and commercial software.  My question is: Is there any software that would meet these requirements and if there is, where could I get it? Asserting that Atheism and Theism are both faith based positions I am recently testing an assertion that I have concluded namely that atheism is a faith based position just like theism is a faith based position.  The reason I arrived at this conclusion is that theists have no proof that God actually exists. It's purely a matter of faith. Yes, there maybe strong implicit proof that God exists in their opinion (scriptures, history, etc) but there is no concrete proof of God's existence. In my view, atheists also suffer from the same problem of providing a proof of their position. Specifically that they cannot prove that God is non-existent.  The typical rebuttal I get is that the burden of proof is on the theists. But I view this as a cop out and they hide behind the wall of burden of proof which is just a bias in the debate.  Given the above, I claim that both atheism and theism are positions based on faith. Would it be incorrect to claim that? What are SPF records, and how do I configure them? For the recently reported production (January 2017) of metallic hydrogen in the laboratory - what is the evidence exactly? My google news page has burst forth the news that metallic hydrogen has been produced in a laboratory using a diamond anvil cell. Only  mentions (at this particular moment) that it has been called into question at - at least - premature. That can be read about in Nature:   Here I only want to ask about the evidence. Is it only the sudden change in visual appearance change as recorded in a camera on top of the microscope, at a specific temperature and pressure? That it "looks shiny?" Or is there actually more direct data than that?  note: I am not asking if the data is sufficient or not, nor if it is convincing, or metallic or not. Just a narrowly defined question about the extent of the observations that have lead to the proposal that a metallic state was achieved.     above: potentially three states of hydrogen as viewed in a diamond anvil cell, from . Cell reference with colour formatting Is it possible to reference a cell in Google Sheets so that cell where it gets displayed also displays it using the same text and cell colour formatting?  =A1   Will only reference cell's value. But if that particular cell has red background and white text I'd like that to be copied as well.  I'm leaning toward existing formula solutions rather than scripts. If applicable of course. Bash: Syntax Error on @() How can I generate valid XML in C#? Help with multirow table I am trying to wrap text in the multirow column (1st one) and only have the vertical lines inside the table if that makes sense.   Can anyone help me? `  \begin{table*}[!htbp] \centering \renewcommand{\arraystretch}{1.4} \begin{tabular}{|c| p{2cm}|c|c|c|c|} \cline{3-6} &amp;&amp;\multicolumn{2}{c|}{\textbf{Gravité du Dommage G1}} &amp; \multicolumn{2}{c|}{\textbf{Gravité du Dommage G2}}\\  \cline{3-6} &amp;&amp;\textbf{Fréquence F1} &amp; \textbf{Fréquence F2} &amp; \textbf{Fréquence F1} &amp; \textbf{Fréquence F2}\\ \hline \multirow{ 2}{*}{\textbf{Probabilité Occurence O1}}&amp;\textbf{Possibilité Evitement P1}&amp;&amp;&amp;&amp;\\ \cline{2-6} &amp;\textbf{Possibilité Evitement P2}&amp;&amp;&amp;&amp;\\ \hline \multirow{ 2}{*}{\textbf{Probabilité Occurence O2}}&amp;\textbf{Possibilité Evitement P1}&amp;&amp;&amp;&amp;\\ \cline{2-6} &amp;\textbf{Possibilité Evitement P2}&amp;&amp;&amp;&amp;\\ \hline \multirow{ 2}{*}{\textbf{Probabilité Occurence O3}}&amp;\textbf{Possibilité Evitement P1}&amp;&amp;&amp;&amp;\\ \cline{2-6} &amp;\textbf{Possibilité Evitement P2}&amp;&amp;&amp;&amp;\\ \hline \end{tabular} \end{table*} Contextually grey out panel element in python 2.8 I have a panel with split column.  In the 2nd row is 3 boolean variables. I want to grey out the 2nd and 3rd option by default. I want the 2nd to be changeable if 1st is true, and 3rd to be changeable if both 1 and two are true. I've read something about "poll()" but not how to actually use it, or set conditions. Physics should only be enablable if singleMesh, and destructable only if physics enabled.      # Create two columns, by using a split layout.     split = layout.split()      # First column     col = split.column()     col.label(text="Building Size:")     col.prop(bpy.context.scene.user_vars, 'buildingHeight')     col.prop(bpy.context.scene.user_vars, 'buildingWidth')     col.prop(bpy.context.scene.user_vars, 'buildingDepth')      # Second column, aligned     col = split.column()     col.label(text="Dynamics:")     col.prop(bpy.context.scene.user_vars, 'singleMesh')     col.prop(bpy.context.scene.user_vars, 'enablePhysics')     col.prop(bpy.context.scene.user_vars, 'destructable_Building')  #EDIT This is what the specific solution to my example looks like. col = split.column() col.label(text="Dynamics:") col.prop(vars, 'singleMesh') sub = col.row() sub.enabled = vars.singleMesh sub.prop(vars, 'enablePhysics') sub = col.row() sub.enabled = vars.enablePhysics sub.prop(vars, 'destructable_Building') I just installed ubuntu 11.10 from a usb stick.   After installation, none of the software which I had collected and run on 11.10 or 11.04 runs on it. Even my newly downloaded opera or chrome installations does not work.  I do not have a internet connection.  Whenever i try to install any .deb file by double clicking it,software center opens up but the install button is grayed out. When running sudo apt-get update I get these following errors:  Err archive.ubuntu.com quantal InRelease Err archive.ubuntu.com quantal-updates InRelease Err archive.ubuntu.com quantal-backports InRelease Err archive.ubuntu.com quantal-security InRelease Err archive.ubuntu.com quantal Release.gpg   Unable to connect to archive.ubuntu.com:http: [IP: 91.189.92.177 80] Err archive.ubuntu.com quantal-updates Release.gpg   Unable to connect to archive.ubuntu.com:http: [IP: 91.189.92.177 80] Err archive.ubuntu.com quantal-backports Release.gpg   Unable to connect to archive.ubuntu.com:http: [IP: 91.189.92.177 80] Err archive.ubuntu.com quantal-security Release.gpg   Unable to connect to archive.ubuntu.com:http: [IP: 91.189.92.177 80] Reading package lists... Done W: Failed to fetch archive.ubuntu.com/ubuntu/dists/quantal/InRelease   W: Failed to fetch archive.ubuntu.com/ubuntu/dists/quantal-updates/InRelease   W: Failed to fetch archive.ubuntu.com/ubuntu/dists/quantal-backports/InRelease   W: Failed to fetch archive.ubuntu.com/ubuntu/dists/quantal-security/InRelease   W: Failed to fetch archive.ubuntu.com/ubuntu/dists/quantal/Release.gpg  Unable to connect to archive.ubuntu.com:http: [IP: 91.189.92.177 80] W: Failed to fetch archive.ubuntu.com/ubuntu/dists/quantal-updates/Release.gpg  Unable to connect to archive.ubuntu.com:http: [IP: 91.189.92.177 80] W: Failed to fetch archive.ubuntu.com/ubuntu/dists/quantal-backports/Release.gpg  Unable to connect to archive.ubuntu.com:http: [IP: 91.189.92.177 80] W: Failed to fetch archive.ubuntu.com/ubuntu/dists/quantal-security/Release.gpg  Unable to connect to archive.ubuntu.com:http: [IP: 91.189.92.177 80] W: Some index files failed to download. They have been ignored, or old ones used instead.   I am using Ubuntu 12.04. This is the command I used after installing Ubuntu from window installer. I am sure my laptop is connected to internet. What can I do now? How to type en-dash and em-dash in Windows 7/8? I write blog posts, and I often need to type en-dash (–) and sometimes em-dash (—) in my blog posts. Currently I keep these characters saved in a text file, and copy-paste them whenever I need them. Unnecessary to say, it is a headache to move between keyboard and mouse when you type large texts.  It would be better for me if there ware a keyboard shortcuts available for these two characters. Is there a way to type en-dash and em-dash in Windows? I use Windows 7 and Windows 8 in different computers.    Here's an aligned comparison of dashes, if you need to see the difference for some reason.   Here's-dash Here's–en-dash Here's—em-dash