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Let A={1,\ 2,\ 3} and R={(1,\ 2),\ (1,\ ...

Let `A={1,\ 2,\ 3}` and `R={(1,\ 2),\ (1,\ 1),\ (2,\ 3)}` be a relation on `A` . What minimum number of ordered pairs may be added to `R` so that it may become a transitive relation on `A` .

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