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

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.