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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.

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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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