Question: Let A be a set and suppose R is a partial order on A (that is, R is a reflexive, transitive, and anti- symmetric relation

Let A be a set and suppose R is a partial

Let A be a set and suppose R is a partial order on A (that is, R is a reflexive, transitive, and anti- symmetric relation on A). For X E A define the cone of 2, denoted (2) R, as follows (2) R = {a A|(a,x) R} Prove that for all 2, Y E A, we have (2) R C (y)R if and only if (x,y) E R

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