in Set Theory & Algebra
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“Every asymmetric relation is antisymmetric”

Is this statement is True or False?


I think it is false, because asymmetric relation never allows loops and antisymmetric relation allows loops.

Am I not correct?

in Set Theory & Algebra
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2 Answers

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you should know the difference between anti symmetric and A symmetric.

anti symmetric says  - if  (x,y) ∈ R then (y,x) ∉ R unless x=y [means it allow those pairs as well in which x and y are equal]

asymmetric says -       if  (x,y) ∈ R then (y,x) ∉ R [ it means he is more strict as he will not allow x=y pairs]

there are some relations which are antisymmetric but not asymmetric but there is no relation which is asymmetric but not antisymmetric.

1 vote
1 vote
I think  this should be  true every asymmetric relation is antisymmetric . but not vice versa.

because in case of antisymmetric diagonal pair are allow. but in case of asymmetric diagonal pair are not allow.

2 Comments

asymmetric doesnot have loops, but antisymmetric may have loop or it maynot be

right?

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yes Right
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