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Define a relation R on the set of positive real numbers by (x, y) R if and only if x 2 y 2 = 0.

  1. Define a relation R on the set of positive real numbers by (x, y) R if and only if x2 y2 = 0. Determine if the relation R is a partial order. If it is not a partial order, explain which property or properties R fails to have.

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