Self-Doubt:Mathematical logic

Question

“Every asymmetric relation is antisymmetric”

Is this statement is True or False?

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

Am I not correct?

Answer 1

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.

Answer 2

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.

Comments

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

right?

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yes Right