Relations

Questions

  • 2

    Doubts on Antisymmetric

    mamteshkumar111@gmail.com
    Reply

    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

    • mamteshkumar111@gmail.com

      Thank you sir!
      for detailed explanation.

  • 3

    relation

    Nikhil Prasad
    Reply

    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

      yes.

    • getgatebook

      symmetric and transitive and anti symmetric and Asymmetric and Irreflexive

  • 0

    Doubt on Irreflexive relations

    sanjayrao
    Reply

    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

  • 1

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

    bambhole
    Reply

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