Given $x y + x z + * y z * +$ recover the tree, write it in usual notation and simplify












1












$begingroup$


Given the boolean expression given in reverse Polish notation $$x y + x z + * y z * +$$ recover the tree, write it in usual notation and simplify.




The usual notation is



$$begin{array}{ll}
&x y + x z + * y z * +\
iff&(x+y) x z + * y z * +\
iff&((x+y)+x) z * y z * +\
iff&(((x+y)+x)*z) y z * +\
iff&(((x+y)+x)*z) (y*z) +\
iff&(((x+y)+x)*z)+(y*z)\
end{array}$$



The recovery tree is



Recovery tree



Finally, the simplification is



$$begin{array}{ll}
&(((x+y)+x)*z)+(y*z)\
iff&(2*x+y)*z+y*z\
iff&2*x*z+y*z+y*z\
iff&2*z*(x+y)
end{array}$$



Is that correct? Is it possible to write $2*xequiv2x$ and so on?



Thanks!






discrete-mathematics trees polish-notation







share|cite|improve this question









$endgroup$








  • 1




    $begingroup$
    Your third line is incorrect: $x~z~+$ translates to $(x+z)$ before it is multiplied by $(x+y)$.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 6:11










  • $begingroup$
    @FabioSomenzi oh, thanks! So it would be $(x+y)*(x+y)+(y*z)$?
    $endgroup$
    – manooooh
    Nov 3 '18 at 6:18








  • 1




    $begingroup$
    The second $x+y$ is actually $x+z$, and then you can simplify a bit.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 6:24






  • 1




    $begingroup$
    It's a Boolean expression, isn't it? So, $+$ is OR and $*$ is AND.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 6:35






  • 1




    $begingroup$
    Right. You should post the answer, because it's your solution. I just gave a little nudge.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 17:35
















1












$begingroup$


Given the boolean expression given in reverse Polish notation $$x y + x z + * y z * +$$ recover the tree, write it in usual notation and simplify.




The usual notation is



$$begin{array}{ll}
&x y + x z + * y z * +\
iff&(x+y) x z + * y z * +\
iff&((x+y)+x) z * y z * +\
iff&(((x+y)+x)*z) y z * +\
iff&(((x+y)+x)*z) (y*z) +\
iff&(((x+y)+x)*z)+(y*z)\
end{array}$$



The recovery tree is



Recovery tree



Finally, the simplification is



$$begin{array}{ll}
&(((x+y)+x)*z)+(y*z)\
iff&(2*x+y)*z+y*z\
iff&2*x*z+y*z+y*z\
iff&2*z*(x+y)
end{array}$$



Is that correct? Is it possible to write $2*xequiv2x$ and so on?



Thanks!






discrete-mathematics trees polish-notation







share|cite|improve this question









$endgroup$








  • 1




    $begingroup$
    Your third line is incorrect: $x~z~+$ translates to $(x+z)$ before it is multiplied by $(x+y)$.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 6:11










  • $begingroup$
    @FabioSomenzi oh, thanks! So it would be $(x+y)*(x+y)+(y*z)$?
    $endgroup$
    – manooooh
    Nov 3 '18 at 6:18








  • 1




    $begingroup$
    The second $x+y$ is actually $x+z$, and then you can simplify a bit.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 6:24






  • 1




    $begingroup$
    It's a Boolean expression, isn't it? So, $+$ is OR and $*$ is AND.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 6:35






  • 1




    $begingroup$
    Right. You should post the answer, because it's your solution. I just gave a little nudge.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 17:35














1












1








1





$begingroup$


Given the boolean expression given in reverse Polish notation $$x y + x z + * y z * +$$ recover the tree, write it in usual notation and simplify.




The usual notation is



$$begin{array}{ll}
&x y + x z + * y z * +\
iff&(x+y) x z + * y z * +\
iff&((x+y)+x) z * y z * +\
iff&(((x+y)+x)*z) y z * +\
iff&(((x+y)+x)*z) (y*z) +\
iff&(((x+y)+x)*z)+(y*z)\
end{array}$$



The recovery tree is



Recovery tree



Finally, the simplification is



$$begin{array}{ll}
&(((x+y)+x)*z)+(y*z)\
iff&(2*x+y)*z+y*z\
iff&2*x*z+y*z+y*z\
iff&2*z*(x+y)
end{array}$$



Is that correct? Is it possible to write $2*xequiv2x$ and so on?



Thanks!






discrete-mathematics trees polish-notation







share|cite|improve this question









$endgroup$




Given the boolean expression given in reverse Polish notation $$x y + x z + * y z * +$$ recover the tree, write it in usual notation and simplify.




The usual notation is



$$begin{array}{ll}
&x y + x z + * y z * +\
iff&(x+y) x z + * y z * +\
iff&((x+y)+x) z * y z * +\
iff&(((x+y)+x)*z) y z * +\
iff&(((x+y)+x)*z) (y*z) +\
iff&(((x+y)+x)*z)+(y*z)\
end{array}$$



The recovery tree is



Recovery tree



Finally, the simplification is



$$begin{array}{ll}
&(((x+y)+x)*z)+(y*z)\
iff&(2*x+y)*z+y*z\
iff&2*x*z+y*z+y*z\
iff&2*z*(x+y)
end{array}$$



Is that correct? Is it possible to write $2*xequiv2x$ and so on?



Thanks!






discrete-mathematics trees polish-notation




discrete-mathematics trees polish-notation






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 3 '18 at 5:48









manoooohmanooooh

5681517




5681517








  • 1




    $begingroup$
    Your third line is incorrect: $x~z~+$ translates to $(x+z)$ before it is multiplied by $(x+y)$.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 6:11










  • $begingroup$
    @FabioSomenzi oh, thanks! So it would be $(x+y)*(x+y)+(y*z)$?
    $endgroup$
    – manooooh
    Nov 3 '18 at 6:18








  • 1




    $begingroup$
    The second $x+y$ is actually $x+z$, and then you can simplify a bit.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 6:24






  • 1




    $begingroup$
    It's a Boolean expression, isn't it? So, $+$ is OR and $*$ is AND.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 6:35






  • 1




    $begingroup$
    Right. You should post the answer, because it's your solution. I just gave a little nudge.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 17:35














  • 1




    $begingroup$
    Your third line is incorrect: $x~z~+$ translates to $(x+z)$ before it is multiplied by $(x+y)$.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 6:11










  • $begingroup$
    @FabioSomenzi oh, thanks! So it would be $(x+y)*(x+y)+(y*z)$?
    $endgroup$
    – manooooh
    Nov 3 '18 at 6:18








  • 1




    $begingroup$
    The second $x+y$ is actually $x+z$, and then you can simplify a bit.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 6:24






  • 1




    $begingroup$
    It's a Boolean expression, isn't it? So, $+$ is OR and $*$ is AND.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 6:35






  • 1




    $begingroup$
    Right. You should post the answer, because it's your solution. I just gave a little nudge.
    $endgroup$
    – Fabio Somenzi
    Nov 3 '18 at 17:35








1




1




$begingroup$
Your third line is incorrect: $x~z~+$ translates to $(x+z)$ before it is multiplied by $(x+y)$.
$endgroup$
– Fabio Somenzi
Nov 3 '18 at 6:11




$begingroup$
Your third line is incorrect: $x~z~+$ translates to $(x+z)$ before it is multiplied by $(x+y)$.
$endgroup$
– Fabio Somenzi
Nov 3 '18 at 6:11












$begingroup$
@FabioSomenzi oh, thanks! So it would be $(x+y)*(x+y)+(y*z)$?
$endgroup$
– manooooh
Nov 3 '18 at 6:18






$begingroup$
@FabioSomenzi oh, thanks! So it would be $(x+y)*(x+y)+(y*z)$?
$endgroup$
– manooooh
Nov 3 '18 at 6:18






1




1




$begingroup$
The second $x+y$ is actually $x+z$, and then you can simplify a bit.
$endgroup$
– Fabio Somenzi
Nov 3 '18 at 6:24




$begingroup$
The second $x+y$ is actually $x+z$, and then you can simplify a bit.
$endgroup$
– Fabio Somenzi
Nov 3 '18 at 6:24




1




1




$begingroup$
It's a Boolean expression, isn't it? So, $+$ is OR and $*$ is AND.
$endgroup$
– Fabio Somenzi
Nov 3 '18 at 6:35




$begingroup$
It's a Boolean expression, isn't it? So, $+$ is OR and $*$ is AND.
$endgroup$
– Fabio Somenzi
Nov 3 '18 at 6:35




1




1




$begingroup$
Right. You should post the answer, because it's your solution. I just gave a little nudge.
$endgroup$
– Fabio Somenzi
Nov 3 '18 at 17:35




$begingroup$
Right. You should post the answer, because it's your solution. I just gave a little nudge.
$endgroup$
– Fabio Somenzi
Nov 3 '18 at 17:35










1 Answer
1






active

oldest

votes


















1












$begingroup$

No, it is not correct. As @FabioSomenzi said in comments, the expression must be $(x+y)*(x+z)+(y*z)$, which has as a tree



Tree



and after applying some properties ends up with $xvee(ywedge z)$.






share|cite|improve this answer









$endgroup$













    Your Answer





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "69"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: true,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: 10,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    noCode: true, onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2982593%2fgiven-x-y-x-z-y-z-recover-the-tree-write-it-in-usual-nota%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    1












    $begingroup$

    No, it is not correct. As @FabioSomenzi said in comments, the expression must be $(x+y)*(x+z)+(y*z)$, which has as a tree



    Tree



    and after applying some properties ends up with $xvee(ywedge z)$.






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      No, it is not correct. As @FabioSomenzi said in comments, the expression must be $(x+y)*(x+z)+(y*z)$, which has as a tree



      Tree



      and after applying some properties ends up with $xvee(ywedge z)$.






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        No, it is not correct. As @FabioSomenzi said in comments, the expression must be $(x+y)*(x+z)+(y*z)$, which has as a tree



        Tree



        and after applying some properties ends up with $xvee(ywedge z)$.






        share|cite|improve this answer









        $endgroup$



        No, it is not correct. As @FabioSomenzi said in comments, the expression must be $(x+y)*(x+z)+(y*z)$, which has as a tree



        Tree



        and after applying some properties ends up with $xvee(ywedge z)$.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 24 '18 at 19:50









        manoooohmanooooh

        5681517




        5681517






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to Mathematics Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid …



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2982593%2fgiven-x-y-x-z-y-z-recover-the-tree-write-it-in-usual-nota%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            -

            Popular posts from this blog

            Bressuire

            Image
            .mw-parser-output .infobox{border:1px solid #aaa;background-color:#f9f9f9;color:black;margin:.5em 0 .5em 1em;padding:.2em;float:right;clear:right;width:22em;text-align:left;font-size:88%;line-height:1.6em}.mw-parser-output .infobox td,.mw-parser-output .infobox th{vertical-align:top;padding:0 .2em}.mw-parser-output .infobox caption{font-size:larger}.mw-parser-output .infobox.bordered{border-collapse:collapse}.mw-parser-output .infobox.bordered td,.mw-parser-output .infobox.bordered th{border:1px solid #aaa}.mw-parser-output .infobox.bordered .borderless td,.mw-parser-output .infobox.bordered .borderless th{border:0}.mw-parser-output .infobox-showbutton .mw-collapsible-text{color:inherit}.mw-parser-output .infobox.bordered .mergedtoprow td,.mw-parser-output .infobox.bordered .mergedtoprow th{border:0;border-top:1px solid #aaa;border-right:1px solid #aaa}.mw-parser-output .infobox.bordered .mergedrow td,.mw-parser-output .infobox.bordered .mergedrow th{border:0;border-right:1px solid ...
            Read more

            Cabo Verde

            Image
              Nota: Cabo-verdiano redireciona para este artigo. Para a língua falada em Cabo Verde, veja crioulo cabo-verdiano. Para outros significados, veja Cabo Verde (desambiguação). Coordenadas: 14° 55' N 23° 31' O Cabo Verde República de Cabo Verde Bandeira Brasão de Armas Lema: Unidade, Trabalho, Progresso Hino nacional: Cântico da Liberdade Gentílico: cabo-verdiano [ 1 ] Capital Praia 14° 55' N 23° 31' O Cidade mais populosa Praia Língua oficial Português Governo República unitária semipresidencialista [ 2 ]  - Presidente Jorge Carlos Fonseca  - Primeiro-ministro Ulisses Correia e Silva História    - Descoberta 1460   - Independência 00 • de Portugal 5 de Julho de 1975   - Multipartidarismo 13 de Janeiro de 1990  Área    - Total 4 033 km² (146.º)  - Água (%) 0,08 População    - Estimativa para 2017 560 899 [ 3 ] hab. (173.º) ...
            Read more

            Gyllenstierna

            Image
            .mw-parser-output .infobox{border:1px solid #aaa;background-color:#f9f9f9;color:black;margin:.5em 0 .5em 1em;padding:.2em;float:right;clear:right;width:22em;text-align:left;font-size:88%;line-height:1.6em}.mw-parser-output .infobox td,.mw-parser-output .infobox th{vertical-align:top;padding:0 .2em}.mw-parser-output .infobox caption{font-size:larger}.mw-parser-output .infobox.bordered{border-collapse:collapse}.mw-parser-output .infobox.bordered td,.mw-parser-output .infobox.bordered th{border:1px solid #aaa}.mw-parser-output .infobox.bordered .borderless td,.mw-parser-output .infobox.bordered .borderless th{border:0}.mw-parser-output .infobox-showbutton .mw-collapsible-text{color:inherit}.mw-parser-output .infobox.bordered .mergedtoprow td,.mw-parser-output .infobox.bordered .mergedtoprow th{border:0;border-top:1px solid #aaa;border-right:1px solid #aaa}.mw-parser-output .infobox.bordered .mergedrow td,.mw-parser-output .infobox.bordered .mergedrow th{border:0;border-right:1px solid ...
            Read more