How to explain that $A \implies B$ is true when $A$ is false I'm teaching my little sister propositional logic per her request.  I was trying to explain to her why $A \implies B$ holds whenever $A$ is false, and I didn't succeed with that.  I referred her to the definition: $A \implies B$ is true if whenever $A$ true, $B$ is true. If $A$ is false, then it is "never" true. If we want to test whether the implication is true, we need to check if $B$ follows when $A$ is true, but $A$ is never true, so we need not check anything, hence the implication is true.   Is my reasoning even correct? I forgot how to do these stuff anyway.   Please help me explain this idea. It would be nice if you can give an intuitive way to think about it as well.
In classical logic, why is $(p\Rightarrow q)$ True if both $p$ and $q$ are False? I am studying entailment in classical first-order logic.  The Truth Table we have been presented with for the statement $(p \Rightarrow q)\;$ (a.k.a. '$p$ implies $q$') is: $$\begin{array}{|c|c|c|} \hline p&amp;q&amp;p\Rightarrow q\\ \hline T&amp;T&amp;T\\ T&amp;F&amp;F\\ F&amp;T&amp;T\\ F&amp;F&amp;T\\\hline \end{array}$$  I 'get' lines 1, 2, and 3, but I do not understand line 4.      Why is the statement $(p \Rightarrow q)$ True if both p and q are False?  We have also been told that $(p \Rightarrow q)$ is logically equivalent to $(~p || q)$ (that is $\lnot p \lor q$).  Stemming from my lack of understanding of line 4 of the Truth Table, I do not understand why this equivalence is accurate.       Administrative note. You may experience being directed here even though your question was actually about line 3 of the truth table instead. In that case, see the companion question  And even if your original worry was about line 4, it might be useful to skim the other question anyway; many of the answers to either question attempt to explain both lines.
Git ignore file for Xcode projects Which files should I include in .gitignore when using Git in conjunction with Xcode? This works perfectly:  $ inotifywait --event create ~/foo Setting up watches. Watches established. /home/ron/foo/ CREATE bar   However, this just sits there when directory tun0 is created under /sys/devices/virtual/net.  $ inotifywait --event create /sys/devices/virtual/net Setting up watches. Watches established.   Since those folders are world readable, I'd expect inotifywait to work.  So, what am I doing wrong?  Thanks When I try to set the default combo for switching to different language layouts in my keyboard from Shift+Super+Space to Alt+Shift I can't.  I used to have this combo since Ubuntu 14 and even before that when I used to have Windows. Now for some stupid reason it does not allow (actually nothing happens its not like I get an error or the combo is used elsewhere). How could I bypass this bug? Greatest and Least Resistance and Current Characteristics of Parallel vs Series circuits Which type of circuit would have the greater resistance?  Which type would have the greater current? and Why?  My book says that parallel has the greater resistance than current as parallel wiring if thought as water pump tubes has greater resistance during water flow.  Contrary to my book, if I make up numbers to solve for which has the greater resistance, i find that  series has greater resistance.  Equivalent resistance of 2 Ohm resistor in series is greater than that of 2 resistors with 2 ohms in parallel. I I have a computer with Windows XP installed.  My user does not have a password.  When Windows starts, it goes to the login screen. Because my user has no password, is there any way to bypass this screen, and log in automatically? Change the Ubuntu program that runs when a command can't be found How can I let a footnote continue on the next page? I have a rather long footnote which breaks a listing in two parts, unnecessarily.  Since the listing is more important then the footnote I'd rather lake to have the footnote split.   Can I customize (one or all) footnotes to have a maximal length before they are continued on the next page? Or can I manually split a footnote in two to get the effect? Why I think tension should be twice the force in a tug of war Google Image Search using Android I have an image on my smartphone and I want to paste it into Google Image Search to see if I can get similar images.  I can do this by pasting the image using desktop but not using Android ...  Is there such a possibility? Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case I am having a difficulty setting up the proof of the fact that two basis of a vector space have the same cardinality for the infinite-dimentional case. In particular, let $V$ be a vector space over a field $K$ and let $\left\{v_i\right\}_{i \in I}$ be a basis where $I$ is infinite countable. Let $\left\{u_j\right\}_{j \in J}$ be another basis. Then $J$ must be infinite countable as well. Any ideas on how to approach the proof? How should I phrase an important question that I need to ask a professor? When needing to ask a professor about something important and potentially delicate, what is an appropriate way to phrase the question or write the email?  Examples include:   Requesting a recommendation letter Asking for exceptions to policy (e.g., ignoring a course prerequisite, rescheduling an exam) Asking if you can do research with them, join a group, get into a program Scheduling a meeting, exam, or defense Letting them know about a change of plans Letting them know about a life event affecting your work or studies (e.g., wedding, funeral, sickness, vacation) Perfect set without rational numbers Sorry if this problem is repeated.  Is there a nonempty perfect set in $\mathbb{R}^1$ which contains no rational number?  Proof sketch: This set must be uncountable because any nonempty perfect set in $\mathbb{R}^k$ is uncountable.   We know that Cantor set (C) is perfect set on a line. If we take $E=C+\sqrt{2}=\{x+\sqrt{2}: x\in C\}$. Will this set be an answer to above problem? I have seen the following methods of putting JavaScript code in an &lt;a&gt; tag:  function DoSomething() { ... return false; }    &lt;a href="javascript:;" onClick="return DoSomething();"&gt;link&lt;/a&gt; &lt;a href="javascript:DoSomething();"&gt;link&lt;/a&gt; &lt;a href="javascript:void(0);" onClick="return DoSomething();"&gt;link&lt;/a&gt; &lt;a href="#" onClick="return DoSomething();"&gt;link&lt;/a&gt;   I understand the idea of trying to put a valid URL instead of just JavaScript code, just in case the user doesn't have JavaScript enabled. But for the purpose of this discussion, I need to assume JavaScript is enabled (they can't login without it).  I personally like option 2 as it allows you to see what's going to be run&ndash;especially useful when debuging where there are parameters being passed to the function. I have used it quite a bit and haven't found browser issues.  I have read that people recommend 4, because it gives the user a real link to follow, but really, # isn't "real". It will go absolutely no where.  Is there one that isn't support or is really bad, when you know the user has JavaScript enabled?  Related question: . Why is integration so much harder than differentiation? How to calculate the distribution of the minimum of multiple exponential variables? $X_1$, $X_2$, $X_3$ are independent random variables, each with an exponential distribution, but with means of $2.0, 5.0, 10.0$ respectively. Let $Y$= the smallest or minimum value of these three random variables. Derive and identify the distribution of $Y$. (The distribution function may be useful).    How do I solve this question? Do I plug in each mean to the exponential distribution? I would appreciate it if someone could explain this to me, thanks. I am trying to use a file repository for updating linux/ubuntu on a non-connected machine. The architecture for this machine (uname -a):  x86_64 GNU/Linux   The results of dpkg --printarchitecture are:  amd64   It is a Trusty Tahr amd64 machine, and it specifically says this, for example, in the aptitude sources.list file. Also, the "About this Computer" in ubuntu specifically says the machine is 64-bit. So, I installed the amd64 packages on the machine. However, when I try to do apt-get update, I get errors such as:  W: Failed to fetch file:/var/spool/apt-mirror-trusty/mirror/archive.ubuntu.com/ubuntu/dists/trusty/main/binary-i386/Packages  File not found   So, in other words, even though it is a 64-bit machine, apt is inexplicably trying to read i386 packages. Why is it doing this and how can I make it use the 64-bit packages?  Note that there is nothing in sources.list that specifies i386.  The only uncommented line in the sources.list file is:  deb file:///var/spool/apt-mirror-trusty/mirror/archive.ubuntu.com/ubuntu trusty main restricted universe multiverse Carrying confidential corporate data into US on laptop/Drive/device - how to prevent data theft? If I travel to the US and had privacy concerns (for instance may be I was afraid that a rogue customs official may steal said data) what is the current recommended best practice to avoid this? I accidentally killed a noble, now every guard wants to kill me. Is there any way I can get rid of the bounty? Autosegmental Representation in tikz-qtree This is what I want to achieve    and this:    But all I've been able to make with tikz-qtree is the following:  \documentclass[12pt,a4]{article} \usepackage[utf8]{inputenc} \usepackage{tipa,tikz,tikz-qtree} \begin{document}  \begin{tikzpicture} [baseline] \tikzset{frontier/.style={distance from root=90pt}} \Tree [.$\sigma$ [.O [ p ] ] [.R [.$\mu$ a ] [.$\mu$ : ] ] ] \end{tikzpicture} \begin{tikzpicture} [baseline] \tikzset{frontier/.style={distance from root=90pt}} \Tree [.$\sigma$ [.O [ p ] ] [.R [.$\mu$ a ]  ] ] \end{tikzpicture}   And this:  \begin{tikzpicture}[baseline] \tikzset{frontier/.style={distance from root=90pt}} \Tree [.$\sigma$ [.O [ l ] ] [.R [.$\mu$ a ] [.$\mu$ l ] ] ] \end{tikzpicture} \begin{tikzpicture} [baseline] \tikzset{frontier/.style={distance from root=90pt}} \Tree [.$\sigma$ [.O [ : ] ] [.R [.$\mu$ a ] [ l ] ] ] \end{tikzpicture} \end{document}   Which renders:    and    The important part here is the linking from the leaves to more than one parent (it would be nice if I had the option of making the line dashed too). Now, pst-asr doesn't quite achieve what I want it to. It's important that I have the moras ('mu's). (Also it's a pstricks package, which means I must typeset it in DVIPSPDF.) I have tried a bit of the forest-package (especially forest-GP1), but I can't make that work as I want either. Lastly, some have recommended xyling, but I find that package very difficult to use.  Any recommendations?  Thanks. Generalization of Hölder inequality