I consider $(P \rightarrow Q) \vee (Q \rightarrow P)$, that is $(\neg P \vee Q) \vee (\neg Q \vee P)$ and so $\neg P \vee Q \vee \neg Q \vee P$, which is a tautology.  It seems strange to me that, given two arbitrary formulas, necessarily  one implies the other or viceversa. (I am thinking for example of this case: P stands for 'Ann loves animals' and Q 'Ann is a student')  Where is my mistake? Perhaps in the interpretation of $P$ and $Q$?  Any clarification will be much appreciated.
I tried to prove that $(p \to q) \lor (q \to p)$ is a tautology.  I used $p$ and $¬q$ as conditions. (Premises 1 and 5)  I managed to get to a solution, but I'm not sure if it's right.  Can you please check it?   Thank you!!!:)
Is there a pattern to which Star Trek ships get the definite article? Some ships in Star Trek are referred to with definite articles. "The Enterprise", "The Defiant". Other ships are referred to without them. "Voyager", "Enterprise". Is there a pattern to or explanation for this behavior? The new top bar is out on meta. Consider it a beta Converting to upper and lower case in Java I'm a Canadian citizen with a Canadian passport. I booked a flight with American Airlines to Mexico City From Toronto Pearson and it says that "Passenger details are needed to check in".  Flight 1: YYZ -> DFW -> MEX Flight 2: MEX -> DFW -> YYZ     They already took my name, gender and such. It is now asking for my passport number and expiry date. That all seems reasonable. However, when I enter that I am a Canadian resident it asks for:  1) Street or hotel in US 2) City in US 3) State in US    My trip to DFW is only for a connecting flight. 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Basically, is there any appreciable difference between:  onchange="javascript: myFunction(this)"   and  onchange="myFunction(this)"   ? I am trying to prove the following by Mathematical Induction:  $$\sum_{i=1}^n i\cdot i! = (n+1)!-1\quad\text{for all integers $n\ge 1$}$$   My proof by Induction follows: First prove $P(1)$ is true,  $$\sum_{i=1}^1 i\cdot i! = (1+1)! - 1$$  Then, for all integers $k &gt;= 1$, if $P(k)$ is true then $P(k+1)$ is also true,  $$ \sum_{i=1}^k i\cdot i! = (k+1)! - 1$$ Then, we must show that $P(k+1)$ is true   $$ \sum_{i=1}^{k+1} i\cdot i! = ((k+1)+1)! - 1\\ \sum_{i=1}^{k+1} i\cdot i! = (k+2)! - 1$$  I am currently struggling with the next step to show that $P(k)$ is equal to $P(k+1)$. How would I finish this prove by induction? Can I do anything about a Nikon d750 taking 5 minutes to power on after taking saltwater damage? I have had a Nikon d750 for a year or so, and 6 months ago it took on a bit of saltwater damage. It still works, but twice in the past it wouldn't power on, once for two weeks and once for two days.   Now it is at a point where it takes around 5 minutes to power on, and when i switch the camera to 'off' or standby, it completely powers off as if the battery drops out, then it takes another 5 mins or so for it to power back on, if it does at all. So I have switched the standby timer in the settings to 'infinity' so it just stays powered on.  I am taking it in to have it looked at, I just hope the damage isn't too fatal. I wonder if anyone has experienced anything similar to this, or can help me diagnose the actual problem. I have tried different batteries, and everything else possible really. Camera itself works fine, just power issues.  thanks in advance. I am using ArcMap 10.1. The background: I have an .mxd that I intend to roll out across the company as our default template for all future maps/figure production. This .mxd contains two Data Frames; the first (&quot;Main&quot;) is larger (occupying almost the entire page) and is designed to be used to hold the majority of mapped data whilst the second (&quot;Inset&quot;) is much smaller and is to be used as an overview map. The problem: When choosing to import this new .mxd to an existing .mxd (using the Change Layout button on the Layout toolbar) the wizard automatically selects the smaller (&quot;Inset&quot;) Data Frame to occupy the larger part of the page. The screenshot below shows this interface with a red box indicating the two possible locations of each Data Frame:  Whilst it is possible to manually alter the order of the Data Frames using the Move Up or Move Down buttons, how do I change the default option for this setting (i.e. so that the &quot;Main&quot; Data Frame always appears in the larger space - &quot;2&quot;)? The reasoning is that I would like the process of using this new .mxd template to be as simple as possible, this is especially important as we have a wide range of users with varying abilities. Does anyone know how to choose/change this default setting? It does not appear to be in the Data Frame Properties &gt; Data Frame menu where I would expect it to be. Windows 7 System process reading/writing like crazy I have a problem that my windows 7 computer sometimes starts accessing the disk like crazy for maybe 10 minutes at a time. The process in question is the "system" process. I have disabled superfetch and hibernation on my computer, if that makes any difference. I disabled those to see if they were the cause of the problems, but no change. I have 6 GB of RAM and only the web browser was started when I took the screenshot, so I don't think it was thrashing due to page faults.  Any ideas on how to find the cause of this? Compute $\iint\limits_R\frac{y}{x+y^2}dA$ where $R=[0,1]\times[1,2]$ Compute $\displaystyle\iint\limits_R\frac{y}{x+y^2}dA$ where $R=[0,1]\times[1,2]$  $\displaystyle\int_0^1\int_1^2\frac{y}{x+y^2}dydx=\int_0^1\int_1^2y(x+y^2)^{-1}dydx$  How do I integrate the denominator if the superscript is $-1$?   Hints are appreciated! Unable to install LanguageTool 2.5 extension for LibreOffice 4.2 on Ubuntu 14.04 I am not able to install LanguageTool extension for LibreOffice. Getting exception when I try to install it.   p.s. Somebody says that the solution is installing openoffice.org-java-common package but Ubuntu 14.04 does not have this package in its repository.  System details:  OS: Ubuntu 14.04 LTS  LibreOffice: 4.2 (4.2.3.3)  LanguageTool: 2.5  Java: Oracle JDK 1.8.0_05     Exception message: What's your preferred way of getting current system status (current CPU, RAM, free disk space, etc.) in Python? Bonus points for *nix and Windows platforms.  There seems to be a few possible ways of extracting that from my search:   Using a library such as  (that currently seems not actively developed and not supported on multiple platform) or something like  (again no activity since 2007 it seems and no support for Windows). Using platform specific code such as using a os.popen("ps") or similar for the *nix systems and MEMORYSTATUS in ctypes.windll.kernel32 (see ) for the Windows platform. One could put a Python class together with all those code snippets.   It's not that those methods are bad but is there already a well-supported, multi-platform way of doing the same thing? Avoiding if statement inside a for loop? To start in or at a company? I am not sure about what is right:     I can start my career at an international company.   or     I can start my career in an international company.   For me at sounds appropriate? Best way to simulate "group by" from bash?