Chapter 8.2, Problem 30ES

In 9-33, determine whether the given relation is reflexive, symmetric, transitive, or none of these. Justify your answer.

Let A be the “punctured plane,”; that is, A is the set of all points in the Cartesian plane except the origin (0,0). A relation R is defined on A as follows: Fro every $p_1$ and $p_2$ in $A,p_{1}R{p}_2\iff p_1$ and $p_2$ lie on the same half line emanating from the origin.