what is the Relationship between Zero nominal interest rates and liquidity traps
The paragraph that you included likely assumes that nominal rates won't go below zero, and therefore that $r_n$>=0 at the zero lower bound. This has been challenged by unconventional monetary and exchange rate policies (i.e. the EU, Switzerland). This likely leads to a few assumptions under classical economic frameworks:

-The Money Demand curve is not horizontally asymptotic at $r_n$=0

-If it is assumed that there is rate mobility below a zero nominal rate (it can go lower and lower with market manipulation), $\frac{d\left(r_n\right)}{d\left(Q_{md}\right)}$≠0 where $r_n$&lt;0. Logically, a -0.41% rate affects consumers differently than does a -0.68% rate (remember that this is effectively the risk free rate; risk premiums will yield positive rates that can be interpreted using classical liquidity preference theory)

This tool has been used for different reasons. Switzerland isn't using negative nominal rates to escape a liquidity trap, but to keep the Franc from appreciating and sending their trade deficit through the roof. The EU on the other hand has resorted to this unconventional monetary policy to try to stimulate growth and avoid a deflationary spiral. They hope to incentivize banks to lend money at the negative rate plus a risk premium rather than be charged to hold money as reserves by the ECB. Consequences exist for these policies, however. Because consumers would rather hold money as cash than lose it in a negative yielding savings account, the money supply of the banking system weakens, and rates can rise back up. Due to its only recent implementation, negative interest rates are likely still considered experimental at best. 

Anyways, the paragraph argues that an above zero inflation target allows more policy flexibility, as $r_r$=$r_n$ when inflation equals zero. This effectively gives borrowers cheaper "real" lending while lenders still gain a rate on their assets above holding money as cash (and therefore no bank runs or contracted money supply). Again, this paragraph is either assuming that the ZLB equals zero, or that negative nominal rates are not sustainable. Mankiw would probably argue that a higher inflation target (which leads to generally higher nominal rates in equilibrium), would've given the EU a better ability to manipulate aggregate demand with a "target" lower bound of 0% nominal interest.