i) For a conductor, there is no gap in between the valence band and conduction band. Thus the band gap energy is almost zero for a conductor. For a semiconductor, there is a small gap in between the valence band and conduction band, and so a semiconductor must have band gap energy.
ii) For this type of problem, we will first make the truth table according to the given waveform. The truth table is shown in the figure, and according to the truth table, the gate is a NAND gate whose logic symbol is as shown in the figure.