Relationship: reflexive, symmetric, antisymmetric, transitive

  • Thread starter nicnicman
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  • #1
nicnicman
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Homework Statement


Determine which binary relations are true, reflexive, symmetric, antisymmetric, and/or transitive.

The relation R on P = {a, b, c} where R = {(a, a), (a, b), (a, c), (b, c), (c, b)}


Homework Equations





The Attempt at a Solution


Not reflexive because there is no (b, b) or (c, c).
Not symmetric because there is (a, b), but not (b, a).
Not antisymmetric because there is (b, c) and (c, b).
Not transitive because there is (b, c) and (c, b) but no (b, b).

Is it possible for there to not be any binary relations?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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Homework Statement


Determine which binary relations are true, reflexive, symmetric, antisymmetric, and/or transitive.

The relation R on P = {a, b, c} where R = {(a, a), (a, b), (a, c), (b, c), (c, b)}


Homework Equations





The Attempt at a Solution


Not reflexive because there is no (b, b) or (c, c).
Not symmetric because there is (a, b), but not (b, a).
Not antisymmetric because there is (b, c) and (c, b).
Not transitive because there is (b, c) and (c, b) but no (b, b).

Is it possible for there to not be any binary relations?

It is a binary relation, but as you say, it doesn't have any of those properties.
 
  • #3
nicnicman
136
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Yeah, that's what I thought. Thanks for the help again.
 

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