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Determine whether each of the following...

Determine whether each of the following relations are reflexive, symmetric and transitive:(i) Relation R in the set `A = {1, 2, 3, ..., 13 , 14}`defined as `R = {(x , y) : 3x y = 0}`(ii) Relation R in the set N o

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Explore conceptually related problems

Determine whether Relation R on the set A={1,\ 2,\ 3,\ ,\ 13 ,\ 14} defined as R={(x ,\ y):3x-y=0} is reflexive, symmetric or transitive.

Is the relation R in the set A={1,2,3,4,5} defined as R={(a,b):b=a+1} reflexive ?

Knowledge Check

  • The relation R defined on the set A = {1,2,3,4, 5} by R ={(x, y)} : |x^(2) -y^(2) | lt 16 } is given by

    A
    {(1,1), (2, 1), (3, 1),(4, 1), (2,3)}
    B
    {(2,2), (3,2),(4,2), (2,4)}
    C
    {(3,3), (3,4), (5,4), (4, 3), (3, 1)}
    D
    None of these

  • R is a relation on the set of N defined as R= {x, y): 2x + y = 24}. Then, the domain of R is:

    A
    `{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22} `
    B
    `{3, 6, 9, 12, 14, 16, 18, 21} `
    C
    `{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} `
    D
    `{4, 8, 12, 14, 16, 18, 20} `

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    Determine whether Relation R on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6} defined as R={(x ,\ y): y is divisible by x} is reflexive, symmetric or transitive.

    The relation R on the set A = {1, 2, 3} defined as R ={(1, 1), (1, 2), (2, 1), (3, 3)} is reflexive, symmetric and transitive.

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