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A relation R is defined on the set z of ...

A relation R is defined on the set z of integers as follows : (x,y) `in RR hArr x^(2) +y^(2) = 25`. Express R and `R^(-1)` as the set of ordered pairs and hence find their respective domains.

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Knowledge Check

  • The relation R defined on a set A = { 0,-1,1,2} by xRy if | x^(2)+y^(2)| lt=2 , then which one of the following is true?

    A
    R= {(0,0),(0,-1),(0,1),(-1,0), (-1,1),(1,2),(1,0)}
    B
    `R^(-1)=` {(0,0),(0,-1),(0,1),(-1,0), (1,0)}
    C
    Domain of R is { 0,-1,1,2 }
    D
    Range of R is { 0,-1,1}

  • Let R be the relation over the set of all straight lines in a plane such that l_(1) Rl_(2) hArr l_(1)bot l_(2) . Then R is

    A
    symmetric
    B
    reflexive
    C
    transitive
    D
    an equivalence relation

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    If w(x, y, z) = x^(2)y + y^(2)z + z^(2)x, x, y, z in RR , Find the differential dw.

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    Show that the relation R in the set Z of intergers given by R ={(a,b):2 divides a-b } is an equivalence relation.

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