Simplify the following symbolic statement

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Simplify the following symbolic statement



$(xgt3)lor(xgt10)$



The answer given is : $(xgt3)$



Why is this the answer?




algebra-precalculus




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    $x>10implies x>3.$
    – mfl
    Aug 19 at 10:23










  • To help you understand what this symbolic statement is about, you can make for yourself een logical table as a function of the variable x. For example for x=2 you see that the statement (x>3) is not true, hence 0. Also (x>10) is not true. Next check the case x=7. And then check x=12. Finally apply the OR operator to the results.
    – M. Wind
    Aug 19 at 19:33















up vote
0
down vote

favorite












Simplify the following symbolic statement



$(xgt3)lor(xgt10)$



The answer given is : $(xgt3)$



Why is this the answer?




algebra-precalculus




share|cite|improve this question


















  • 2




    $x>10implies x>3.$
    – mfl
    Aug 19 at 10:23










  • To help you understand what this symbolic statement is about, you can make for yourself een logical table as a function of the variable x. For example for x=2 you see that the statement (x>3) is not true, hence 0. Also (x>10) is not true. Next check the case x=7. And then check x=12. Finally apply the OR operator to the results.
    – M. Wind
    Aug 19 at 19:33













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Simplify the following symbolic statement



$(xgt3)lor(xgt10)$



The answer given is : $(xgt3)$



Why is this the answer?




algebra-precalculus




share|cite|improve this question














Simplify the following symbolic statement



$(xgt3)lor(xgt10)$



The answer given is : $(xgt3)$



Why is this the answer?





algebra-precalculus





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 20 at 16:09









Asaf Karagila♦

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293k31408736










asked Aug 19 at 10:21









stochasticmrfox

216




216







  • 2




    $x>10implies x>3.$
    – mfl
    Aug 19 at 10:23










  • To help you understand what this symbolic statement is about, you can make for yourself een logical table as a function of the variable x. For example for x=2 you see that the statement (x>3) is not true, hence 0. Also (x>10) is not true. Next check the case x=7. And then check x=12. Finally apply the OR operator to the results.
    – M. Wind
    Aug 19 at 19:33













  • 2




    $x>10implies x>3.$
    – mfl
    Aug 19 at 10:23










  • To help you understand what this symbolic statement is about, you can make for yourself een logical table as a function of the variable x. For example for x=2 you see that the statement (x>3) is not true, hence 0. Also (x>10) is not true. Next check the case x=7. And then check x=12. Finally apply the OR operator to the results.
    – M. Wind
    Aug 19 at 19:33








2




2




$x>10implies x>3.$
– mfl
Aug 19 at 10:23




$x>10implies x>3.$
– mfl
Aug 19 at 10:23












To help you understand what this symbolic statement is about, you can make for yourself een logical table as a function of the variable x. For example for x=2 you see that the statement (x>3) is not true, hence 0. Also (x>10) is not true. Next check the case x=7. And then check x=12. Finally apply the OR operator to the results.
– M. Wind
Aug 19 at 19:33





To help you understand what this symbolic statement is about, you can make for yourself een logical table as a function of the variable x. For example for x=2 you see that the statement (x>3) is not true, hence 0. Also (x>10) is not true. Next check the case x=7. And then check x=12. Finally apply the OR operator to the results.
– M. Wind
Aug 19 at 19:33











1 Answer
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The statement $(x gt 3 ) cup ( x gt 10 )$ given by you, is basically -




$x$ is greater than 3 OR $x$ is greater than 10




written in symbolic form.



Now, it should be obvious to you that $( x gt 10 ) Rightarrow ( xgt 3 )$ , as pointed out by @mfl in the comments. Thus, the statement reduces to



$( x gt 3 ) cup ( x gt 10 ) = x :x gt 3 or x gt 10 =x: xgt 3=( x gt 3)$



Now, take a look at the logic provided by @M. Wind. Once, you realize how the interaction of the two conditions with the 'OR' operator renders the second condition meaningless, the result is trivial and obvious.



Basically, whenever $x$ is greater than 10, it is already greater than 3; and the OR statement means that we only have to check for the truth of one condition, which in this case is $xgt 3$. Another way of looking at it is that $xgt 3 $ already contains both the conditions, allowing us to neglect $x gt 10$ as already contained in $xgt 3$ by virtue if the 'OR' condition.






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    1 Answer
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    The statement $(x gt 3 ) cup ( x gt 10 )$ given by you, is basically -




    $x$ is greater than 3 OR $x$ is greater than 10




    written in symbolic form.



    Now, it should be obvious to you that $( x gt 10 ) Rightarrow ( xgt 3 )$ , as pointed out by @mfl in the comments. Thus, the statement reduces to



    $( x gt 3 ) cup ( x gt 10 ) = x :x gt 3 or x gt 10 =x: xgt 3=( x gt 3)$



    Now, take a look at the logic provided by @M. Wind. Once, you realize how the interaction of the two conditions with the 'OR' operator renders the second condition meaningless, the result is trivial and obvious.



    Basically, whenever $x$ is greater than 10, it is already greater than 3; and the OR statement means that we only have to check for the truth of one condition, which in this case is $xgt 3$. Another way of looking at it is that $xgt 3 $ already contains both the conditions, allowing us to neglect $x gt 10$ as already contained in $xgt 3$ by virtue if the 'OR' condition.






    share|cite|improve this answer


























      up vote
      1
      down vote













      The statement $(x gt 3 ) cup ( x gt 10 )$ given by you, is basically -




      $x$ is greater than 3 OR $x$ is greater than 10




      written in symbolic form.



      Now, it should be obvious to you that $( x gt 10 ) Rightarrow ( xgt 3 )$ , as pointed out by @mfl in the comments. Thus, the statement reduces to



      $( x gt 3 ) cup ( x gt 10 ) = x :x gt 3 or x gt 10 =x: xgt 3=( x gt 3)$



      Now, take a look at the logic provided by @M. Wind. Once, you realize how the interaction of the two conditions with the 'OR' operator renders the second condition meaningless, the result is trivial and obvious.



      Basically, whenever $x$ is greater than 10, it is already greater than 3; and the OR statement means that we only have to check for the truth of one condition, which in this case is $xgt 3$. Another way of looking at it is that $xgt 3 $ already contains both the conditions, allowing us to neglect $x gt 10$ as already contained in $xgt 3$ by virtue if the 'OR' condition.






      share|cite|improve this answer
























        up vote
        1
        down vote










        up vote
        1
        down vote









        The statement $(x gt 3 ) cup ( x gt 10 )$ given by you, is basically -




        $x$ is greater than 3 OR $x$ is greater than 10




        written in symbolic form.



        Now, it should be obvious to you that $( x gt 10 ) Rightarrow ( xgt 3 )$ , as pointed out by @mfl in the comments. Thus, the statement reduces to



        $( x gt 3 ) cup ( x gt 10 ) = x :x gt 3 or x gt 10 =x: xgt 3=( x gt 3)$



        Now, take a look at the logic provided by @M. Wind. Once, you realize how the interaction of the two conditions with the 'OR' operator renders the second condition meaningless, the result is trivial and obvious.



        Basically, whenever $x$ is greater than 10, it is already greater than 3; and the OR statement means that we only have to check for the truth of one condition, which in this case is $xgt 3$. Another way of looking at it is that $xgt 3 $ already contains both the conditions, allowing us to neglect $x gt 10$ as already contained in $xgt 3$ by virtue if the 'OR' condition.






        share|cite|improve this answer














        The statement $(x gt 3 ) cup ( x gt 10 )$ given by you, is basically -




        $x$ is greater than 3 OR $x$ is greater than 10




        written in symbolic form.



        Now, it should be obvious to you that $( x gt 10 ) Rightarrow ( xgt 3 )$ , as pointed out by @mfl in the comments. Thus, the statement reduces to



        $( x gt 3 ) cup ( x gt 10 ) = x :x gt 3 or x gt 10 =x: xgt 3=( x gt 3)$



        Now, take a look at the logic provided by @M. Wind. Once, you realize how the interaction of the two conditions with the 'OR' operator renders the second condition meaningless, the result is trivial and obvious.



        Basically, whenever $x$ is greater than 10, it is already greater than 3; and the OR statement means that we only have to check for the truth of one condition, which in this case is $xgt 3$. Another way of looking at it is that $xgt 3 $ already contains both the conditions, allowing us to neglect $x gt 10$ as already contained in $xgt 3$ by virtue if the 'OR' condition.







        share|cite|improve this answer














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        edited Aug 20 at 16:11

























        answered Aug 20 at 16:06









        DevashishKaushik

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