Boolean Function question I need to know how I can prove this question.  Prove that not every boolean function is equal to a boolean function constructed by only using And ($\wedge$) and Or ($\vee$)
Not every boolean function is constructed from $\wedge$ (and) and $\vee$ (or) Prove that not every boolean function is equal to a boolean function constructed by only using $\wedge$ and $\vee$.  Here is my solution, can I ask for a feed back on my solution please?   $p∧q$                          $0 0 0 1 $   $p∨q$  $0 1 1 1$  Not every boolean function is the same when using $ ∨ $ and $∧.$  Edited part!  $p\vee q$                  $0111$  $(p\vee q)\wedge p = p$  $0 = 0$  $0 = 0$  $1 = 1$  $1 = 1$  $(p\vee q)\vee p = p\vee q$  $0 = 0$  $1 = 1$  $1 = 1$  $1 = 1$  here is my edited answer , can I ask for more feed back , thanks
In what cases I should skip 's in possessive case? How to measure time taken by a function to execute I need to get execution time in milliseconds.  I originally asked this question back in 2008. The accepted answer then was to use  However, we can all agree now  that using the standard  API is more appropriate. I am therefore changing the accepted answer to this one. Set the default permission when creating a file Is there a way in javascript to detect if the unload event is caused via a refresh, the back button, or closing the browser? $$\displaystyle\int \:\sin^n\left(x\right)\cos^m\left(x\right)\mathrm  dx=\frac{\sin^{n+1}x\cos^{m-1}x}{m+n}+\frac{m-1}{m+n}\int \:\sin^nx\cos^{m-2}x\,\mathrm dx$$  I have been trying to solve for over a week now can someone please help me. How to not count blank pages in frontmatter of two-sided document Python program to calculate harmonic series Does anyone know how to write a program in Python that will calculate the addition of the harmonic series. i.e. 1 + 1/2 +1/3 +1/4... What is the definition of $2.5!$? (2.5 factorial) I was messing around with my TI-84 Plus Silver Edition calculator and discovered that it will actually give me values when taking the factorial of any number $n/2$ where $n$ is any integer greater than $-2$. Why does this happen? I thought factorials were only defined for positive integers and $0$, so what is my calculator doing to get the answer $3.32335097$ when I enter $2.5!$? Is there actually a definition of $2.5!$ or is my calculator just being weird? How is the factorial function implemented?  I understand the binary implications of $2.5$, so that could possibly have something to do with it. I get a domain error when trying to take the factorial of $-1, 2.3, e$, and any number that is not of the form $n/2$ where $n$ is any integer greater than $-2$. How do I reset the Windows XP Administrator password? I have forgotten the Administrator password of my Windows XP installation and locked out. Is there a way to reset it? I do have physical access to the PC. What are "first class" objects? When are objects or something else said to be "first class" in a given programming language, and why? In what do they differ from languages where they are not?  EDIT. When one says "everything is an object" (like in Python), does he indeed mean that "everything is first-class"? I tried the following code to replace QQ with ZZ, but it doesn't do what I want:  var1=QQ sed -i 's/$var1/ZZ/g' $file   However, this code does what I want:  sed -i 's/QQ/ZZ/g' $file   How do I use variables in sed? How to find a program which is preventing sleeping? I am noticing that recently my laptop does not go to sleep/lockout after its configured X minutes of inactivity like it did in the past. I suspect some program (like media player does) is preventing it from going to sleep. I do not have any media player running, so how can I find which program is preventing it from sleeping?  It does go to sleep if I close the lid. But I would also like for it to go to sleep after X minutes of inactivity.  Update: Upgraded to Ubuntu 18.04 with default Gnome and Wayland enabled. If random variables are drawn from an identical distribution, why doesn't this guarantee they are independent? EDIT Like some comments below are remarking the table environment doesn't allow tables over more than one page. However the solution works fine  I need to make a table over more than one page. The standard approach seems to be to use the ltablex environment. However, it doesn't work; also I assume that the table environment may also be required for the thesis template I work on (e.g. suppose for the capture).   \documentclass[11pt]{article} \usepackage{booktabs} \usepackage{tabularx} \usepackage{ltablex}  \begin{document}  \begin{table} \caption{Example of an table} \label{tab:daypack}      \begin{tabularx}{\linewidth}{@{}cX@{}}   \toprule \textbf{Column 1} &amp; \textbf{Column 2} \\[6pt] \midrule \endhead $R$ &amp; 1This is an example sentence \\[6pt] $R$ &amp; 2As well as the line before \\[6pt] $A$ &amp; 3Also this is an example \\[6pt] $R$ &amp; 4This is an example sentence \\[6pt] $R$ &amp; 5As well as the line before \\[6pt] $A$ &amp; 6Also this is an example \\[6pt] $R$ &amp; 7This is an example sentence \\[6pt] $R$ &amp; 8As well as the line before \\[6pt] $A$ &amp; 9Also this is an example \\[6pt] $R$ &amp; 10This is an example sentence \\[6pt] $R$ &amp; 11As well as the line before \\[6pt] $A$ &amp; 12Also this is an example \\[6pt] $R$ &amp; 13This is an example sentence \\[6pt] $R$ &amp; 14As well as the line before \\[6pt] $A$ &amp; 15Also this is an example \\[6pt] $R$ &amp; 16This is an example sentence \\[6pt] $R$ &amp; 17As well as the line before \\[6pt] $A$ &amp; 18Also this is an example \\[6pt] $R$ &amp; 19This is an example sentence \\[6pt] $R$ &amp; 20As well as the line before \\[6pt] $A$ &amp; 21Also this is an example \\[6pt] $R$ &amp; 22This is an example sentence \\[6pt] $R$ &amp; 23As well as the line before \\[6pt] $A$ &amp; 24Also this is an example \\[6pt] $R$ &amp; 25This is an example sentence \\[6pt] $R$ &amp; 26As well as the line before \\[6pt] $A$ &amp; 27Also this is an example \\[6pt] $R$ &amp; 28This is an example sentence \\[6pt] $R$ &amp; 29As well as the line before \\[6pt] $A$ &amp; 30Also this is an example \\[6pt] $R$ &amp; 31This is an example sentence \\[6pt] $R$ &amp; 32As well as the line before \\[6pt] $A$ &amp; 33Also this is an example \\[6pt] $R$ &amp; 34This is an example sentence \\[6pt] $R$ &amp; 35As well as the line before \\[6pt] $A$ &amp; 36Also this is an example \\[6pt] $R$ &amp; 37This is an example sentence \\[6pt] \bottomrule \end{tabularx}    \end{table}      \end{document} Possible Duplicate:          I would like to use round parentheses () instead of square brackets [] for citations in a document that I'm working on.   I figured out how to get them in the text using the round option with natbib.  I can't figure out to have the generated bibliography to show () instead of [] when it lists the references.  What do I need to change to fix the way it formats the bibliography? If I have bought X tickets, do I have X hand baggage allowances? If I have bought 3 tickets for the same flight, can I bring three times the cabin allowance allowed per ticket?  The way I see it I am doing the airline a favor  Related: Does metric signature affect the stress energy tensor? Do I need a UK or Ireland transit visa when flying from the US to a Schengen country? I am travelling to Budapest and therefore have a Schengen Visa. I hold an Indian passport and a valid US visa. I'm travelling from Chicago-Heathrow-Budapest and returning by Budapest-Dublin-Chicago.  Would I need a transit visa for UK/Ireland?  UPDATE  Hoping this will help someone someday.   I was not allowed to board my return flight (BUD-DUB-ORD) because I do not hold an overnight Irish Transit Visa. They said I could have transited happily if the connecting flight was in the same day, but because I would have to originally land at 10 PM and catch the connecting flight next morning at 10 AM, I needed a transit visa. Well, I thought it was BS, but couldn't help comply with the rules. I booked another last minute ticket and flew via Warsaw via LOT. In reading I am not sure if the issue below could have something to do with needing a custom wordpress ajax handler? All of these functions are inside my functions.php file. I have a couple of PHP functions that are supposed to pass information from one to another. The an AJAX call to the final function should produce the final result through that call. Its not happening. My count results in 0 and I am not understanding why. If I replace my query with a static array like [44,55,99,33] then it will pass the values ok. Likewise if I keep the query and simply replace the $id in the query and make it a static id such as '20' then it works. I would think that the id was the issue then and it wasnt pulling properly but it seems to work ok just not pass? function idx(){     global $wpdb, $id;       $getId = $_SERVER['REQUEST_URI'];     $ecp = explode('/', $getId);     if($ecp[3] != ''){         $id = $ecp[3];     }         return $id; } add_action( 'after_setup_theme', 'idx' );  =============================================== function Total_Result(){     global $wpdb;     $id = idx();        /*$resultx = [44,88,59,52];*/ ;      $resultx = $wpdb-&gt;get_results( $wpdb-&gt;prepare(&quot;SELECT * FROM {$wpdb-&gt;prefix}custom_form_submission_conversation as cc LEFT JOIN {$wpdb-&gt;prefix}custom_form_submission as cs on cc.fsid ='$id' WHERE fsid='$id'&quot; ));          $resultxs = array($resultx);          $total_result =  count($resultxs[0]);     echo  $total_result; }  when I var_dump $resultx I get: array(3) { [0]=&gt; object(stdClass)#1256 (36) { [“cid”]=&gt; string(3) “167” [“fsid”]=&gt; string(2) “20” [“specified_date”]=&gt; string(3) “yes” [“price_quote”]=&gt; string(4) “1140” [“posted_by”]=&gt; string(9) “dc_vendor” [“limit_count”]=&gt; string(1) “1” [“read_unread”]=&gt; string(1) “1” [“vendor_response”]=&gt; string(4) “zero” [“date_created”]=&gt; string(19) “2021-04-15 11:39:08” }   [1]=&gt; object(stdClass)#1257 (36) { [“cid”]=&gt; string(3) “186” [“fsid”]=&gt; string(2) “20” [“specified_date”]=&gt; string(3) “Yes” [“price_quote”]=&gt; string(3) “602” [“posted_by”]=&gt; string(8) “customer” [“limit_count”]=&gt; string(1) “1” [“read_unread”]=&gt; string(1) “1” [“vendor_response”]=&gt; string(4) “zero” [“date_created”]=&gt; string(19) “2021-04-15 11:39:08” }   [2]=&gt; object(stdClass)#1258 (36) { [“cid”]=&gt; string(3) “188” [“fsid”]=&gt; string(2) “20” [“specified_date”]=&gt; string(3) “yes” [“price_quote”]=&gt; string(4) “1017” [“posted_by”]=&gt; string(9) “dc_vendor” [“limit_count”]=&gt; string(1) “1” [“read_unread”]=&gt; string(1) “0” [“vendor_response”]=&gt; string(4) “zero” [“date_created”]=&gt; string(19) “2021-04-15 11:39:08” } }   so then I try and pass that data like so: function getvendorresponsestatus() {     global $wpdb; $id = idx();          $total_resultx = Total_Result($id);         die; }  Ive tried with and without the die();. The AJAX call is: setInterval(function(){     var ffiidd = jQuery('#ffiidd').val();     var ajaxurl = &quot;&lt;?php echo admin_url('admin-ajax.php'); ?&gt;&quot;;          jQuery.post(ajaxurl, {         action: &quot;vendorAjaxprog&quot;,         ffiidd: ffiidd     }, function(data) {         console.log(data);         jQuery.post(ajaxurl, {             action: &quot;getvendorresponsestatus&quot;, //&lt;&lt;&lt;&lt;&lt;&lt;&lt;&lt; this is the action that calls the function             fsid : ffiidd         },         function(datas) {             console.log('+ datas);             jQuery('.cust_vendor_top').html(datas);         });         if(data == 0){}else{             jQuery('.ajaxreload').html(data);                                     }     });               }, 5000);/*==30 seconds==*/  So the question is why wont it pass along the query array information but it passes a basic array or it will pass if I change the id in the query to be static? I know the query is good because of when I var_dumped it, I have results before I get to the Total_Result() function. How do I craft command blocks? I went to my friends house, and he was playing Minecraft on the PC. He showed me a command block, but when I went home and opened Minecraft pocket edition, I went to the crafting table but I could not find any command blocks to craft.  What are command blocks and how do I craft them?