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The relation R defined in A= {1,2,3} by ...

The relation R defined in A= {1,2,3} by a R b if `|a^(2)-b^(2)| le 5`. Which of the following is not true?

A

Domain of `R={1,2,3}`

B

Range of R= {5}

C

`R^(-1)= R`

D

R= {(1,1),(2,2),(3,3),(2,1),(1,2),(2,3),(3,2)}

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • The relation R defined on the set A = { 1, 2, 3, 4} by : R= {( x,y) : |x^(2)-y^(2)| le 10, x,y in A} is given by :

    A
    {(1,1) , (1. 2), (1,3) ,(1, 4), (2, 1), (2, 2), (2, 3), (2, 4)}
    B
    {(1, 1), (1, 2), (1, 3), (2, 2), (2, 3), (3, 3), (3, 4), (4, 4)}
    C
    {(1, 1), (1, 2), (1, 3), (2,1), (2, 2), (2,3), (3,1), (3, 2), (3, 3), (3,4), (4, 3), (4, 4)}
    D
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  • f: R to R and g: [0,oo)to R is defined by f(x) = x^(2) and g(x) = sqrtx . Which one of the following is not true?

    A
    gof (4) = 4
    B
    fog (2) = 2
    C
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    D
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  • Let R be a relation in the set of natural numbers defined by R= {(1+x,1+x^(2)) : x le 5, x in N} . Which of the following in false :

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    B
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    D
    At least one is false

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