• 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

  • 1

    Doubt on Irreflexive relations


    Sir,Suppose i have a set A={1,2,3} and a relation R on Set A is given as {(1,1,),(2,2)},now this is clearly not reflexive,can we say that this relation is irreflexive because not all the elements that are required to satisfy the reflexive property are present here

    • getgatebook

      yes. (some how we have missed your question. )

  • 1

    last Statement of this video(1:25:00)


    Suppose R = {(1,1)} which is symmetric and transitive but not reflexive.
    This may also a counter example of statement 3 ??

  • 2



    aRb, you are mapping only 1R1,2R2, but why not from 1R2, 1R3 like this then it wont be reflexive, please clear this?

    • getgatebook

      Still it is reflexive. Reflexive relation should have (1,1) ,(2,2)…(n,n). It also can have other elements. ( {1,2,3,…n} is domain)

    • rajeshwarpro

      got it (a,a)