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Define an equivalence relation....

Define an equivalence relation.

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Similar Questions

Explore conceptually related problems

Show that the relation R in the set of all natural number, N defined by is an R = {(a , b) : |a - b| "is even"} in an equivalence relation.

Prove that the relation R in the set of integers Z defined by R = {(x,y) : x - y. is an integer) is an equivalence relation.

Knowledge Check

  • Let A= {a,b,c}. Which of the following is not an equivalence relation in A?

    A
    `R_(1)= {(a,b),(b,c),(a,c),(a,a)}`
    B
    `R_(2)= {(c,b),(c,a),(c,c),(b,b)}`
    C
    `R_(3)= {(a,b),(b,b),(c,c),(a,b)}`
    D
    None of these

    • Similar Questions

    Explore conceptually related problems

    Show that the relation R in the set A= {1,2,3,4,5} given by R= "{"(a,b):|a-b| is even} is an equivalence relation.

    Show that the realtion R in the set A of all the books in a library of a collage, given by R = {(x,y):x and y have same number of pages} is an equivalence relation.

    Prove that the relation R in the set of integers z defined by R = { ( x , y) : x-y is an integer } is an equivalence relation.

    Statement-1: The relation R on the set N xx N defined by (a, b) R (c, d) iff a+d = b+c for all a, b, c, d in N is an equivalence relation. Statement-2: The intersection of two equivalence relations on a set A is an equivalence relation.

    Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L _(1) , L _(2)) : L _(1) is parallel to L _(2)}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x +4.

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    Show that the relation R in the set A={1,2,3,4,5} given by R={(a,b) : |a-b| is even}, is an equivalence relation.

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