Chapter 3.5, Problem 4EQ

In Exercises 1-4, let S be the collection of vectors in $\left[\begin{array}{l}x\\ y\end{array}\right]in{ℝ}^2$ that satisfy the given property. In each case either prove that S forms a subspace of ${ℝ}^2$ or give a counterexample to show that it does not.

$xy\ge 0$