Relationship: reflexive, symmetric, antisymmetric, transitive

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Homework Statement


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

The relation R on all integers where aRy is |a-b|<=3


Homework Equations





The Attempt at a Solution


The relationship is reflexive because any number minus itself will be zero which is less than 3.
The relationship is symmetric because whenever |a-b|<=3 then |b-a|<=3 is also true.
The relationship is not antisymmetric. Consider (2, 1) and (1, 2). Int his case, |2-1|<=3 and |1-2|<=3.
The relationship is not transitive. Consider (4, 1) and (1, 0). |4-1|<=3 and |1-0|<=3, but |4-0| is not <= 3.

I just want to make sure I'm understanding this correctly. Is this right or am I missing something? I can't think of a case where the relationship wouldn't be symmetric.
 
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  • #2
Dick
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Homework Statement


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

The relation R on all integers where aRy is |a-b|<=3


Homework Equations





The Attempt at a Solution


The relationship is reflexive because any number minus itself will be zero which is less than 3.
The relationship is symmetric because whenever |a-b|<=3 then |b-a|<=3 is also true.
The relationship is not antisymmetric. Consider (2, 1) and (1, 2). Int his case, |2-1|<=3 and |1-2|<=3.
The relationship is not transitive. Consider (4, 1) and (1, 0). |4-1|<=3 and |1-0|<=3, but |4-0| is not <= 3.

I just want to make sure I'm understanding this correctly. Is this right or am I missing something? I can't think of a case where the relationship wouldn't be symmetric.

Those all look correct to me.
 
  • #3
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Thank you for the reassurance.
 

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