• 2

    Doubts on Antisymmetric

    Hi Sir,

    Doubt may not be up to mark.

    Suppose there is a set ‘A’ contains element {1, 2, 3} then

    is Rel^n {(1,2)} is antisymmetric?

    As per the definition if xRy and yRx then x=y for all x,y belong to A.

    but here only xRy is in relation , how it will be antisymmetric. I think there must be at least one ordered pair in the form xRx. I may wrong, please correct me.

    • getgatebook

      definition is in the form of p–>q (yes?)
      if yes then read below line
      definition is true means p–>q is true (yes ?)
      if yes read below line
      p–>q is true then either p = false or p=T and q=T.
      in your example xRy and yRx is p and x=y is q
      substitute (1,2) in the definition
      x=1 and y=2
      then p will become false, So over all p–>q is true
      so definition is true


      Thank you sir!
      for detailed explanation.

  • 3


    Nikhil Prasad

    sir among all 6 type of relation. how many relations satisfies ’empty set’ condition also.

    • getgatebook

      are You asking ” How many properties are satisfied by empty relation?”

    • Nikhil Prasad


    • getgatebook

      symmetric and transitive and anti symmetric and Asymmetric and Irreflexive