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(a) Let R be the relation on Z defined b...

(a) Let R be the relation on Z defined by aRb if and only if `a-b` is an integer. Find: (i) R (ii) domain of R (iii) range of R.
(b) Let R be the relation on Z defined by: `R = {(a,b) : a in Z, b in Z, a^(2) = b^(2)}`
Find (i) R (ii) domain of R (iii) range of R.

Answer

Step by step text solution for (a) Let R be the relation on Z defined by aRb if and only if a-b is an integer. Find: (i) R (ii) domain of R (iii) range of R. (b) Let R be the relation on Z defined by: R = {(a,b) : a in Z, b in Z, a^(2) = b^(2)} Find (i) R (ii) domain of R (iii) range of R. by MATHS experts to help you in doubts & scoring excellent marks in Class 11 exams.

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Knowledge Check

  • Let R be the relation on Z defined by R = P(a,b) : a,b in Z , a-b is an integers}. then

    A
    domain of R is {2,3,4,5,.....}
    B
    range of R is Z
    C
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    D
    None of the above

  • Let A = {(1,2,3,4,6} and R be the relation on A defined by R = {(a,b) : a, b in A, b is divisible by a} Then, R is

    A
    {(1,1),(1,2),(1,3),(1,4),(1,6),(2,2),(2,4),(2,6),(3,3),(3,6),(4,4),(6,6)}
    B
    {(1,1),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4)}
    C
    {(1,1),(1,3),(2,4),(2,6),(3,3),(3,6),(4,6)}
    D
    None of the above

  • Let R_(1) be a relation defined by R_(1)={(a,b)|agtb,a,b in R} . Then R_(1) , is

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

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