Double boolean negation operator
Double Negation in C++
I'm studying for an abstract algebra exam and one of the review questions was this:     Let $X$ be a set, and $\mathcal P(X)$ be the power set of $X$. Consider the operations $\Delta$ = symmetric difference (a.k.a. "XOR"), and $\bigcap$ = intersection.   a) Does $\Delta$ and $\bigcap$ make $P(X)$ into a ring?   b) If so, is it a ring with unity?   c) Is the ring commutative?   d) Is it a field?   For parts a) and b), I think it does form a ring with unity, but I'm not quite sure how to get started on proving it.   For part c), it is a commutative ring since $\mathcal P(X)$ is closed under symmetric difference and intersection, right?  Not even sure how to get started on d).  I'd really like to understand this question fully, so any kind of input would be tremendously helpful. Thank you! Light Presets .exr I would like to install light presets for Blender to automate my lightning in my scenes. I have some .exr files (from Greyscalegorilla) but I don't know how to do it on Blender to make it work. Can someone help me? Thank you How to use multiple Effect Strips in Blender Video Sequence Editor? How can I tell what RAM will fit my computer? If I want to add more RAM to my computer, how can I buy something compatible? What kinds are there? How do I determine which kind my computer will accept and how much I can add? Network button missing gone from Nautilus? I'm using Ubuntu 16.04.3 LTS.  I remember having a link in Nautilus that I used to browse network shares with in the past. I don't remember exactly but I think it was "Windows network" or "Browse network".  Now I can't find this on my current installation, there's only "Connect to server", but this is not what I want. Is there a way to put that link there? Do conjugate priors just lead to a posterior that is a modification of the parameters of the prior? We know, for example, that the conjugate relationship between the classic beta-binomial is as follows:  \begin{align}  y &amp;∼ \mathcal{Bin}(n,\ θ)  \\  θ &amp;∼ \mathcal{Beta}(α,\ β)  \\ θ|y &amp;∼ \mathcal{Beta}(y + α,\  n − y + β) \end{align}  Notice how the posterior is just a change in parameterization compared to the prior. Is the posterior of conjugate priors just a change in parameters? These may be separate questions, but the following MWE:    \usepackage{pdfpages} ...   \addcontentsline{lot}{subsection}{\ref{tab:UserRoles} \textbf{User Roles}}   \includepdf[pages={-}, pagecommand={\label{tab:UserRoles}}, offset=0in -1in, addtolist={9, table, {The User Roles table}, tab:UserRoles}]{UserRolesTable}   ...   has several unexpected behaviors.   I get the following warning:  Package pdfpages Warning: There's something wrong with the entries of `addtolist'. Not all entries were processed. Check `addtolist' [in the MWE]."    Probably due to the \label not being bound to the inserted pdf (in a table environment), my inserted PDF is numbered using the section, and not the expected "Table X" value.   The manually-inserted LoT line (which also uses the section number rather than the incremented table number) is not formatted like the other lines in the LoT - the number lines up, but the table caption itself is not aligned with the others in the list.   The source PDF has no errors and displays correctly in the output PDF.  PDFLaTeX -> BibTex    MWE:  \documentclass[11pt,letterpaper,twoside,final]{article} \usepackage{pdfpages} \begin{document} \listoftables \begin{center} \textbf{Table \ref{tab:UserRoles} - The User Roles Table} \addcontentsline{lot}{subsection}{\ref{tab:UserRoles}  \textbf{User Roles}} % manual entry in ToC  \includepdf[pages={-}, pagecommand={\label{tab:UserRoles}}, offset=0in -1in, addtolist={9, table, {The User Roles table}, tab:UserRoles, lot}]{UserRolesTable} \end{center} \end{document} Create taxonomy terms on the fly How can I find out if Ubuntu supports a particular hardware component, that is, if it works in Ubuntu?  I am going to put together a computer and I am choosing components.   How do I know if Ubuntu supports this or that motherboard, or this or that sound card, or this or that graphics card, etc? How do I know that there is no conflict in Ubuntu between this and that hardware component?   What resources are there to help with such situations?  I know that there are computers with Ubuntu pre-installed and that there are  for whole computers but this is not what I'm looking for. I'm looking for resources to find out support for particular hardware components and conflicts among particular hardware components. Where to find my Favorites in Google Chrome? I'm new to LaTeX and I'm trying to figure out how to correctly format a proof. Can someone show me a basic template for how to do this?   The part I am having the most trouble with is creating new columns and customizing alignment... for instance, how do I add a right-aligned annotation (i.e. by distributive property) to a line of this sample proof? Should I use eqnarray* or is there a better option?  \begin{proof}   Let $t,u \in \mathbb{R}$ where $t=xy$ and $u=zw$. So,   \begin{eqnarray*}     4xyzw &amp;=&amp; 2\cdot2tu \\     &amp;\le&amp; 2\cdot(t^2+u^2) \\     &amp;=&amp; 2\cdot((xy)^2+(zw)^2) \\     &amp;=&amp; 2\cdot(x^2y^2+z^2w^2) \\     &amp;=&amp; 2x^2y^2+2z^2w^2 \\     &amp;\le&amp; ((x^2)^2+(y^2)^2)+((z^2)^2)+(w^2)^2) \\     &amp;=&amp; x^4+y^4+z^4+w^4   \end{eqnarray*} \end{proof} Detecting start bit in software UART I'm experimenting with writing a software UART on my microcontroller using GPIO pins. This is to temporarily add a UART channel on a project until we get the new design implemented that uses a uC with more UART ports.  What I'm having difficulty with is correctly detecting a start bit in a serial stream. The source of the stream is external and doesn't care when my device powers up. So it's very likely that my device will power on and start seeing data bits in the middle of a byte transmission. Undoubtedly, that will cause my software UART to read erroneous values, as it won't be able to tell the difference between a start bit and any other high-to-low transition.  Is this an inevitable issue with a UART channel? Or is there some clever trick that the uC manufacturers use in their hardware UARTs? Reproducible LaTeX builds - compile to a file which always hashes to the same value Why can two (or more) electric field lines never cross? Bootstrap Paradox in Interstellar Broken URL for data.stackexchange.com help page How do I keep Python print from adding newlines or spaces? In python, if I say  print 'h'   I get the letter h and a newline.  If I say   print 'h',   I get the letter h and no newline.  If I say  print 'h', print 'm',   I get the letter h, a space, and the letter m.  How can I prevent Python from printing the space?  The print statements are different iterations of the same loop so I can't just use the + operator. Monitor hard drive changes to files Several months ago I saw someone using an application that showed him files on the computer being modified in real time.  Basically there was an application that wasn't working correctly, so he installed the program, ran the application, and saw all the various files that the application either read from or wrote to.  He found out the application was writing a large debugging file it shouldn't be, which ended up being the problem.  I don't remember the application or the name of the person who used it, but I believe it's a freeware application.  Does anyone know what this program might be? Inequality: $ab^2+bc^2+ca^2 \le 4$, when $a+b+c=3$. Let $a,b,c $ are non-negative real numbers, and $a+b+c=3$.  How to prove inequality $$ ab^2+bc^2+ca^2\le 4.\tag{*} $$    In other words, if $a,b,c$ are non-negative real numbers, then how to prove inequality $$ 27(ab^2+bc^2+ca^2)\le 4(a+b+c)^3.\tag {**} $$ $\color{gray}{\mbox{(Without using "universal" Lagrange multipliers method).}}$  Thanks! Ask to install program after "The program 'x' is currently not installed" If you try to execute a program that is not installed you will get a message  The program 'x' is currently not installed. You can install it by typing:  sudo apt-get install x   and instead of offering you to install the program for you, you have to type the actual command. How can this behavior be changed?