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A relation R is defined from the set of ...

A relation R is defined from the set of integer Z to Z as follows:
`(x,y) in Z hArr x^(2) + y^(2)=25`
(i) Express R and `R^(-1)` as the set of ordered pairs.
(ii) Write the domain of R and `R^(-1)`.

Text Solution

Verified by Experts

The correct Answer is:
`R=R^(-1)={(0,5),(0,-5),(3,4),(3,-4),(-3,4),(-3,-4),(4,3),(4,-3), (-4,3),(-4,-3),(5,0),(-5,0)}`
Domain R=Domain `R^(-1)={-5,-4,-3,0,3,4,5}`
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Knowledge Check

  • A relation R is defined in the set Z of integers as follows (x, y ) in R iff x^(2) + y^(2) = 9 . Which of the following is false ?

    A
    R = { (0,3), (0,-3), (3,0), (-3,0)}
    B
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    D
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    B
    Domain of R = {-3,0,3}
    C
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    D
    None of the above

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