I'm currently working on the following question: "At least one of Plato and Democritus believed in the theory of forms. Plato believed in the theory of forms only if he was not an atomist, and Democritus was an atomist only if he did not believe in the theory of forms. Democritus was an atomist. Prove, using Natural Deduction, that Plato was not an atomist" I have been working for quite some time to take the information and turn it into a set of literals and statements I can work with.  So far I have got  P: Plato believed in the theory of forms. D: Democritus believed in the theory of forms. X: Plato was an atomist. Y: Democritus was an atomist.  (PVD), (-X-->P) , (-D--->Y), Y  I don't know where I should start from. Which begs the question, if my literals are wrong. Any help would be much appreciated.
I'm currently working on the following question:  "At least one of Plato and Democritus believed in the theory of forms. Plato believed in the theory of forms only if he was not an atomist, and Democritus was an atomist only if he did not believe in the theory of forms. Democritus was an atomist. Prove, using Natural Deduction, that Plato was not an atomist"  I have been working for quite some time to take the information and turn it into a set of literals and statements I can work with.  So far, I have got $P \lor D$,  $P \Rightarrow \lnot a$,  $D \Rightarrow A$,  $D = A$  However, I cannot seem to make these prove the statement using natural deduction, any hints?
How to determine the maximum number to pass to make -j option? How can I bind arguments to a Python method to store a nullary functor for later invocation?  Similar to C++'s boost::bind.  For example:  def add(x, y):     return x + y  add_5 = magic_function(add, 5) assert add_5(3) == 8 Proving Pascal's Rule : ${{n} \choose {r}}={{n-1} \choose {r-1}}+{{n-1} \choose r}$ when $1\leq r\leq n$ Making SSD & HDD work together like a hybrid Local TLD vs. .com and .com/nl vs .nl I basically have 2 questions about local TLD vs .com.  First question: There already exists a website "keyword.nl" with a crappy website, no SEO optimisation. Is it possible for a website "keyword.com" to rank higher than the "keyword.nl" website on "google.nl" when searching for "keyword"? Or will it always display the .nl website higher because it's a local TLD and the URL consists entirely and only from the searched keyword and it's searched on the .nl version of google?  Second question: I know it's good for SEO to have many websites link to your website. But I also read that local TLD's will score higher on that specific google TLD (.fr website will rank higher in google.fr, etc.) With both those facts in mind, is it better to create a "keyword.com/fr/" and "keyword.com/nl/" website or a "keyword.fr" and a "keyword.nl" website? (In other words, .com/langauge for more links to the website, or a "keyword.local-TLD" website for every different language version of the website) Or maybe even a subdomain? ("fr.keyword.com?")  Kinda new to this, so thanks in advance!  --Edit: additional info--  The reason that I phrased the original question like this is because I wanted to keep the question strictly "webmaster-side". However I feel like maybe I should clarify the background of this question more thoroughly, so the question becomes more clear, and thus the answer. But I don't know if this would make the question a more legal one instead of a "webmaster" one, so please correct me if this is the wrong place to post this question.  I'm a student working on websites in my sparetime, I have basic knowledge about SEO, but that was all local, for companies operating only in one country. However this time a friend contacted me who wants to found a company called "X" (e.g). He wants to ship/operate to multiple countries, but he will first found it (and he himself) lives in The Netherlands (.nl). However there already exists a company in The Netherlands called "x" with the website "x.nl". As far as I understood, the fact that both the companies are called "x" doesn't matter, in trademark/company registery terms, since they are both operating in different work sectors.    But the main issue here is, could my friends website "x.com/nl" outrank the "x.nl" on "google.nl" if you only search on the brand name; "x"?  @Closetnoc:  Hi, thanks a lot for your answer, it gave me some clarification however I feel you misunderstood my first question because of my use of "keyword.com" as an example URL. So I don't really know what conclussion I should draw from your first answer. I updated my question with additional info to clarify it more broadly. From your second answer this is what I understand: A .nl URL will not do that great on google.com, however a .com URL can do just as well as a .nl search on google.nl? So considering the info above, it's best to go with a x.com/fr and a x.com/nl URL, right? Please correct me if I misunderstood. However, if so, that still leaves the first question, if a "x.nl" is already taken, could a "x.com/nl" still outrank it at "google.nl"? I want to make a long shadow just like in this image.  I can create this shadow with shapes and by deleting the unwanted shadows after rasterizing the layer. But it's not very reusable. I can't resize the layer after rasterizing it.  Is there any easy way to make a long shadow like in the image below? Is the Cantor set made of interval endpoints? Windows update giving error 80070002 and manual update not working how to update? I have been trying to update my pc from 20h1 to 20h2 but the windows update shows error message 80007002 and when I manually install the update using windows 10 update assistant it downloads completely and then even starts install and gets stuck at 87 percent on the screen where it says do not turn off. What to do? This is the log file. Matching Profile found: FindRollbackFailure - 3A43C9B5-05B3-4F7C-A955-88F991BB5A48 SetupDiag version: 1.6.0.0 System Information:     Machine Name =      Manufacturer =      Model =      HostOSArchitecture = 1033     FirmwareType = UEFI     BiosReleaseDate = 20160513000000.000000+000     BiosVendor = A12     BiosVersion = A12     HostOSVersion = 10.0.19041     HostOSBuildString = 19041.1.amd64fre.vb_release.191206-1406     TargetOSBuildString = 10.0.19041.621 (vb_release_svc_prod1.201014-1758)     HostOSLanguageId =      HostOSEdition = CoreSingleLanguage     RegisteredAV = Quick Heal Internet Security     FilterDrivers = FileInfo     UpgradeStartTime = 12/20/2020 2:54:38 PM     UpgradeEndTime = 12/20/2020 5:30:40 PM     UpgradeElapsedTime = 02:36:02     CV = Pi3IdU3SlEqpFx93     ReportId =    Error: SetupDiag reports rollback failure found. Last Phase = Pre OOBE Boot Last Operation = OOBE boot apply Error = 0xC1900101-0x4000D LogEntry:   Refer to &quot;https://docs.microsoft.com/en-us/windows/desktop/Debug/system-error-codes&quot; for error information.  Last Setup Phase: Phase Name: Pre OOBE Boot     Phase Started: 12/20/2020 4:37:50 PM     Phase Ended: 1/1/0001 12:00:00 AM     Phase Time Delta: 00:00:00     Completed Successfully? False   Last Setup Operation: Operation Name: OOBE boot apply     Operation Started: 12/20/2020 4:37:50 PM     Operation Ended: 1/1/0001 12:00:00 AM     Operation Time Delta: 0:00:00:00.0000000     Completed Successfully? False Understanding the proof for showing that there are infinitely many $n\in\mathbb{Z}^+$ such that $n!+1$ is divisible by at least two distinct primes There is another post pertaining to this question; however, the other post does not address some specifics that concern me in the proof. Proof: Let $n=p-1, p \geq 7$. Then $p|(p-1)!+1$. We will show that $(p-1)!+1=p^n$ has no solutions. Suppose not. Suppose $(p-1)! + 1 = p^n$ has a solution for $p\geq 7$. Then $(p-1)! =p^n-1  = (p-1)(p^{n-1}+\cdots+p+1)$. So $(p-2)!\equiv n (\mod p-1)$. Now suppose that $(p-1)|n$. Then $p-1\leq n$. So $(p-1)!+1&lt;p^{p-1}\leq p^n$. Hence, there are no solutions. It remains to show that $(p-1)|(p-2)!$. But $p-1=2m$ means $2m|(p-2)!$. QED  Questions:  My understanding is that at the start of the proof, Wilson's theorem is used to show that at least one prime divides $n!+1$.  Why do we want to show that $(p-1)!+1=p^n$ has no solutions? The way I see it is that $p^n$ is composite, and we are basically saying that $p^n\nmid (p-1)!+1$, so no composite number divides $n! +1$. But how and where in the proof do we actually show that another prime $q \neq p$ divides $n!+1$?    Thanks in advance. Extend or remove Data Explorer timeout I know that we don't have automatic login for the Data Explorer, but what's with the automatic timeout/logout?  There have been times that I am logged into the site, maybe I walk away for a little bit, and I come back to being logged out.    Is there a reason for logging us out of Data Explorer?  If so, is it possible to either remove the timeout or extend the period of time before timeout? Removing all 'stable' theme's CSS from a Drupal 8 custom theme I would like to remove all CSSs automatically included from stable theme:  /core/themes/stable/css/system/components/*   I can remove them one by one inside the .info.yml file:  stylesheets-remove:   - 'core/themes/stable/css/system/components/ajax-progress.module.css'   - 'core/themes/stable/css/system/components/autocomplete-loading.module.css'   - ...   Is there a way to remove all of them at once?   Something like:  stylesheets-remove:   - 'core/themes/stable/css/system/components/*' Wireless connection fails every few minutes Does "make offline" option in Google Maps works with applications that utilize Google Maps? In newer Google Maps I can make area available offline.  Do other applications that rely on Google Maps (utilize Google Maps Android API) use offline maps? Why aren't logarithms defined for negative $x$? date difference in days, in Android How to make a drive NTFS from EXT4? I want to know how to make a drive ( non-system ) from EXT4 to NTFS. Can anyone help me out? About an Hour ago, I faced a problem and tried different ways to solve it.  At last I was going to post my Question on Stack Overflow, but the last trick which came in my mind worked, and the problem got resolved.    Now, if I want to post that problem on Stack Overflow with the solution which worked for me, for the purpose to help other newbies to get their answer if they face the same problem, what is the proper way of posting such solution to a problem? gain admin access to sql express 2008 Finite ring has only zero divisors and units If a nonzero element $a$ of a ring $\mathbb{D}$ does not have a multiplicative inverse, then $a$ must be a zero divisor.   If $\mathbb{D}$ has finitely many elements, then the statement is true. However, I don't see why, as for the infinite case, 7 isn't a zero divisor only because every element $a &gt; 0$ when multiplied by a $b &gt; 0$ gives you $ab &gt; 0$ which has nothing to do with infinity or finite amounts of elements. Why do I always hear remote train horn at night? This is definitely not an illusion, as many people have the same experience. I have usually lived in places miles away from train stations, which makes it unlikely to hear any train horns during the day. However at night, occasionally train horns can be heard. I hope if any one can explain the physics of this effect, like possibly sound travels faster at low temperature.