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The relation R on the set N of all natur...

The relation `R` on the set `N` of all natural numbers defined by `(x ,\ y) in RhArrx` divides `y ,` for all `x ,\ y in N` is transitive.

Text Solution

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Let `x R y`, `x R z` i.e., `x` divides `y` & `y` divides `z`.
Let `y = ax & z = by`
where x divides y & y divides z. `⇒ z = by = b(ax) = abx`
∴ x divides z. `=> x R z`. ...
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Knowledge Check

  • The relation ''is a factor of'' on the set N of all natural number is not

    A
    reflexive
    B
    symmetric
    C
    antisymmetric
    D
    transitive

  • If a relation R on the set N of natural numbers is defined as (x,y)hArrx^(2)-4xy+3y^(2)=0,Aax,yepsilonN . Then the relation R is

    A
    reflexive
    B
    symmetric
    C
    transitive
    D
    an aquivalence relation

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