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Thread: Draw directed graph; state if relation is reflexive, transitive, or symmetric.

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    Question Draw directed graph; state if relation is reflexive, transitive, or symmetric.

    For the following relation, draw the corresponding directed graph. State if the relation is reflexive, transitive, or symmetric.

    . . .[tex]\mbox{(a) }\, R\, =\, \{(a,\, 1),\, (b,\, 1),\, (c,\, 1)\}\, \mbox{ over the set }\, \{1,\, 2,\, 3,\, 4,\, 5,\, a,\, b,\, c\}[/tex]



    Cant draw its mapping either please help
    Last edited by stapel; 11-30-2017 at 03:48 PM. Reason: Typing out the text in the graphic; creating useful subject line.

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    Quote Originally Posted by sita View Post
    For the following relation, draw the corresponding directed graph. State if the relation is reflexive, transitive, or symmetric.

    . . .[tex]\mbox{(a) }\, R\, =\, \{(a,\, 1),\, (b,\, 1),\, (c,\, 1)\}\, \mbox{ over the set }\, \{1,\, 2,\, 3,\, 4,\, 5,\, a,\, b,\, c\}[/tex]



    Cant draw its mapping either please help
    Please provide any example of the Transitive Property over any set.
    Last edited by stapel; 11-30-2017 at 03:48 PM. Reason: Copying typed-out graphical content into reply.
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

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    Are you saying you can't draw the directed graph? Please explain where you get stuck in doing that. All it involves is drawing arrows between some of the points in the set { 1, 2, 3, 4, 5, a, b, c }.

    As for the transitive property, that is often the hardest of the properties to be sure of; can you show how you have tried to determine it? There is something different about this relation that could be the source of your difficulty, but I'd want to see your explanation before assuming that is it.

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    I can draw the graph a, b and c map to 1 but not sure why it's transitive.

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    You may be hung up on the issue I saw, but you aren't saying enough to be sure. Can you tell us what you have done to determine whether it is transitive? What do you expect to see in a transitive relation, that you are not seeing?

    Here is a long discussion of the issue I have in mind.

  6. #6
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by sita View Post
    I can draw the graph a, b and c map to 1 but not sure why it's transitive.
    On what basis had you concluded that this relation is transitive? Have you answered the questions about reflexivity and symmetricity?

    When you reply, please show your work and reasoning so far. Thank you!

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