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

sita

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

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



Cant draw its mapping either please help
 
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tkhunny

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

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



Cant draw its mapping either please help
Please provide any example of the Transitive Property over any set.
 
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Dr.Peterson

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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.
 

sita

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

Dr.Peterson

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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.
 

stapel

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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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