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Let R be the relation in the set Z of in...

Let R be the relation in the set Z of integers given by R={(a,b):2 divides a-b}. Show that the relation R transitive ? Write the equivalence class [0].

Text Solution

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Let 2 divides `(a-b)` and 2 divides `(b-c)` : where `a,b,c, in Z`
So 2 divides `[(a-b)+(b-c)]`
2divides `(a-c)` : Yes relation R is transitive
`[0]={0,+-2,+-4,+-6,....}`
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Knowledge Check

  • Let R be the relation in the set N given by R = {(a,b):|a-b| is odd}. Then:

    A
    `(0,1) in R`
    B
    `(2,3) in R`
    C
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    D
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    A
    `(2,3)inR`
    B
    `(4,6)inR`
    C
    `(3,9)inR`
    D
    `(7,24)inR`

  • Let R be the relation in the set of integers Z given by R = {(a, b): 2 divides a - b}. Assertion (A): R is a reflexive relation. Reason (R): A relation is said to be reflexive x Rx, AA x in Z .

    A
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    C
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    D
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