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Prove that the relation R defined on the...

Prove that the relation R defined on the set of real numbers R as `R = {(a,b) : a le b^(2) AA a, b in R}` is neither reflexive nor symmetric nor transitive.

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Show that the relation R is the set of real numbers R defined as R= {(a, b): a le b^(2) } is neither reflexive, nor symmetric, nor transitive.

Show that the relation S in the set R of real numbers defined as S={(a,b): a, b in R and a le b^(3) } is neither reflexive, nor symmetric, nor transitive.

Knowledge Check

  • Let us define a relation R on the set R of real numbers as a R b if a ge b . Then R is

    A
    an equivalence relation
    B
    reflexive, transitive but not symmetric
    C
    symmetric, transitive but not reflexive
    D
    neither transitive nor reflexive but symmetric

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