My teacher proved that following formula is not tautology in intuitionistical logic: $$\neg(p\wedge q)\Leftrightarrow (\neg p\vee\neg q)$$ Is it sufficient to show (and we try to do it) that $$\neg(p\wedge q)\Rightarrow (\neg p\vee\neg q)$$   is not tautology. My teacher wrote red and black formulas. My formulas are green  - there are formulas that to my eye my teacher forgot to write. I know that teacher give arbitrar Kripke model. Tell me please: 1. If my green "supplement" is correct ? 2. From what my teacher conclude red formulas ?  When it comes to black things I know that it is about kripke model.
Show Kripke's model proving that the following formula isn't tautology in intuitionistic logic. $ \neg ( p \wedge q ) \implies (\neg p \vee \neg q) $  Please help/hint me ;)
Multiple Bluetooth speakers simultaneously I would like to pair two sticky dude Bluetooth speakers, at one time with my iPhone. With two of them at once it would be like stereo sound. Is there an app or something maybe? Find all solutions of the equation $n^m=x^2+py^2$ which satisfy the following properties Prove or disprove that,     There always exists a solution of the equation, $$n^m=x^2+py^2$$ with odd $x$ and $y$ and for all $m\geq k$ for some positive integral $k$. Here $p$ is an odd prime and $n\in 2\mathbb{N}$. Is $k$ dependent on $n$? If so then find a way to calculate the value of $k$.   This is basically one of my conjecture which I am trying to prove for quite sometime. Unfortunately, I have progressed very little in this problem. So far I have been only able to prove that for all $m\geq3$ , $n=2$ and $p=7$ there is always a solution of the equation meeting the constraints.   Any idea how to tackle the problem?    Update  After D. Burde's answer of the original problem (see below) I am now interested in finding all $(n,m,p)$ triplets such that the equation holds. Any ideas regarding this problem? Influence of charged particle's own electric field on itself I read this in my textbook: A charged particle or object is not affected by its own electric field.  Since I find this completely unintuitive and my mind is yelling "wrong! wrong! how could a particle even distinguish between its own field and the external fields?" I would really like to hear an explanation about why this is true, if it is.  (A corollary question that comes to my mind after thinking about this is... What about gravity and mass considering the analogous situation? And the other two forces?) How do I select all but two types of entities in Minecraft with the type selector? I've asked this question towards a developer for Minecraft and I thought I'd ask here too since they might not see the question.  How do I select all but two types of entities in Minecraft?  For example, something like: /say @e[type=![Player,Item],r=50] (to clarify I also tried type=Item,Player, type=Item,type=Player etc)  Should select any entity that does not match players or items, so things like Creepers, Ghasts, XPOrbs, PrimedTNT and so on within a radius of 50 blocks and print them to the chat.  Instead it ignores one of the flags, and works with the other instead. How to split bibliography into "works cited" and "works not cited"? I need two bib-like sections: a "References" giving works explicitly cited in my text, and a "Bibliography" (or "Further reading" if you prefer) giving everything from my bibfile that didn't already appear in "References". The first is of course completely standard, but the second... I'm stumped.  Further loose constraints: I'm somewhat committed to biblatex and the biblatex-apa style. But I'll happily accept an answer not related to them if there's any chance I can adapt it. What is wrong with this proof?    Is $\pi=4?$ "Where" exactly are complex numbers used "in the real world"? Possessive form of coordinated noun phrases? Which of the following is accurate in British English to describe our own wedding?        Alex and Jen's Wedding   Alex's and Jen's Wedding   Alex and Jens' Wedding Is there a term denoting the writing of words using numbers instead of letters? Probability of asymmetric random walk returning to the origin Consider the random walk $S_n$ given by $ S_{n+1} =  \left\{   \begin{array}{l}     S_n+2 &amp; \text{with probability $p$}\\     S_n - 1 &amp; \text{with probability $1-p$}   \end{array} \right. \ $  Assume that $S_0 = n &gt;0 $. What is the probability of eventually reaching the the point $0$?  Seems that the probability for this must be less than one; since it is not symmetric, it is not guaranteed to reach the origin if $p&gt;0.5$. It also seems like the positive starting value not being at the origin matters too, but I'm not sure how to compute the probability of eventually reaching the origin. Possible to lock focal length on zoom lens? (SELP1650) (This could turn out to be a bone, practical, product-specific query, but this is the internet so the worst that could happen is a 0 rather than a 1.)  Anyhoo: is it possible to lock a zoomable lens to a certain focal length? Is this a typical feature for a lens?  I want to keep my SELP1650 at X mm to help with some creative experiments, but the thing shifts whenever I move my hand against the lens ring. Does SELP1650 (or the body, Sony A6000) specifically have this option?  Or... is there a reasonably non-goofy DIY trick I could pull off, without bricking the thing? (anticipating a sarky 'duct tape' suggestion) How to convert standard IP address format string to hex and long? I accidentally unset all the directories of $PATH while trying to add a new one in ~/.bashrc. I opened a new terminal window as I was editing and now $PATH is empty. I'm worried if I boot from another drive to find the $PATH I won't be able to boot into this drive again.  Basically, what is the default result of echo $PATH? I have been given the task to rewrite a function as a sum of an even and an odd function. But when I went to analyze the parts of the original function I noticed that one part was neither even nor odd.   The original function was: $g(x) = (x + 1) / (x^2 - 3x + 4$)  After analyzing I realized that when using f(-x) to determine symmetry it produced a 'neither' result. How would I go about writing a function that is neither even nor odd as an even function. (It would have to be an even function as the (x+1) part of the original function is odd and since I need to write it as a sum of even and odd, the denominator would need to be even. Does a polymorphed creature remember who his friends are? I know SO's policy is &quot;you don't have to register to ask questions,&quot; but there are so many new members and so many hit-and-runs... The majority of the questions I see now are coming from new users (i.e., it's their first question). Although unregistered users should still be able to ask questions, I think we should encourage users to create an account. Here is a couple of ways we could do that:  Explicitly encourage people to get an account: there's currently nothing telling people to do that. Maybe tell people something like &quot;Get an account, it's easy!&quot; and maybe show some of the perks of having an account (and having rep).  Maybe give a few bonus points for registering; and have that enable a basic privilege. It could be taken from one of the , for example.   Of course getting people to register is just half of the battle. I don't know what the stats are on this, but I think there's a number of users who create multiple accounts anyways. We could curb that by:  Having smart(er)? duplicate account detection systems, alerting someone who is about to create a new account and possibly has an account already. Give them a message like &quot;Hey, it looks like you already have  account, are you sure you want to create a new one?&quot;  Create a new privilege (10k? 20k?) that gives users tools to detect possible duplicate accounts, eg: &quot;List users with the same e-mail,&quot; &quot;List users with the same IP addresses,&quot;  etc. (without revealing said emails and IPs). Then the 10k/20k can look at other stuff (e.g.: posts) and refer the new user to a moderator for a possible merge. First off I did try the power options setting and it's on 'Never' but that did nothing. The drive still spins down after 15-20 seconds of not being used. I need it to spin all the time because it's more efficient with my way of using it. Also listening to music from that drive is absolutely destroying the drive making it spin up and down all the time causing immense wear and tear. Any ideas on how to stop it from spinning down? Please don't suggest bat files that keep creating editing a file.  &nbsp;  Oh and here is the model of the drive: wdc wd10jpvx-22jc3t0 and my OS is Windows 10 64 bit. Learning Resources on Parsers, Interpreters, and Compilers I've been wanting to play around with writing my own language for a while now (ostensibly for the learning experience) and as such need to be relatively grounded in the construction of Parsers, Interpreters, and Compilers. So:   Does anyone know of any good resources on constructing Parsers, Interpreters, and Compilers?   EDIT: I'm not looking for compiler-compilers/parser-compilers such as Lex, Yacc and Bison... I accidentally deleted a file from my laptop. I'm using Fedora. Is it possible to recover the file? How does the bounty system work? It's possible to offer and award bounties of reputation on questions.   What is a bounty? How can I find questions that have a bounty attached? How do I start a bounty? When can I start a bounty? Why is the system requiring me to choose a bounty amount that's higher than the minimum? Can I use Markdown formatting in the bounty remarks? Can I edit the remark? How long is the bounty period? How do I award a bounty? Can I award a bounty to my own answer? Can I award a bounty to an old answer? If I offer a bounty on someone else's question, can I award the bounty to their answer? After awarding the bounty, can I remove it or move it to another answer at a later time? What happens if there's no answer after the bounty period? What happens if I feel my question is still unanswered? What is automatic awarding? Are bounty awards exempt from the 200 points/day reputation limit? How does Community Wiki mode affect bounties? How does user deletion or post dissociation affect bounties? Can I award a bounty to an answer from a deleted user or one where the author was dissociated? Can I offer a second bounty after the first one has expired? Can I raise my bounty? What happens if a bounty question is closed or deleted? Why can't I vote to close or migrate a bounty question? What happens if I delete my account while I have an active bounty? Do I keep an awarded bounty when I delete my answer? What happens if a question where I awarded a bounty later gets deleted or migrated? Can I cancel my bounty? Can I affect / divide / share part of my bounty to two (or more) users? How many outstanding bounties can a single user have?      See also:  in the Help Center