Answer to No.1

a) Vgs > VTn

The n-channel MOSFET is turned ON by applying a Gate-Source bias, Vgs, which is more positive than the Threshold voltage, VTn. That is, ON if Vgs > VTn.  This is because the sufficiently 'positive' Vgs (i.e., Vgs more positive than VTn) can attract enough negatively-charged carriers (electrons) to the channel region.

The channel region is the semiconductor area under the gate electrode.

You can verify that Vgs > VTn when NMOS is ON :

for example,

• apply logic 1 (red) to Vin. The NMOS is closed (ON).
• Then, the Vg = Vin >= VIH = 3.5 V (@ Vcc = 5.0 V).  Thus, Vgs = Vg - Vs >= 3.5 V.
• The VTn is, for example, 2.5 V (check it by dragging VTn a little).
• Thus, Vgs > VTn.
• This is true for a range of Vcc, Vin, and VTn.