1) Let \(p(x,y) = \begin{cases} x + y &\quad \text{if } x \ge 0 \text{ and } y \ge 0, \\ x - 2y &\quad \text{if } x < 0 \text{ and } y < 0, \\ 3x + y &\quad \text{otherwise}. \end{cases} \)

What is p(p(1,-1),p(-5,-2))?

2) How many positive integers \(n\le 2009\) have the property that \(\lfloor{\log_2(n)}\rfloor\) is odd?]

Thanks!

Guest Aug 10, 2019