Proof

• Monotonicity translates to \(a \leq b \implies a \leq b\) and is trivially true.

• Need to show: \(a \leq_P b \implies g(f(a)) \leq_R g(f(b))\)

  • The monotonicity of \(f\) gives us \(f(a) \leq_Q f(b)\) and the monotonicity of \(g\) gives us the result we need.