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Let R be a relation on the set A of orde...

Let R be a relation on the set A of ordered pairs of positive integers defined by `(x ," "y)" "R" "(u ," "v)` if and only if `x v" "=" "y u` . Show that R is an equivalence relation.

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We observe the following properties of `R`.

Reflexivity : Let `(a, b)` be an arbitrary element of the set `A`. Then,

`(a, b)` in` A `

`Rightarrow a b=b a `

`Rightarrow(a, b) R(a, b)`

Thus, `R` is reflexive on `A`.

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