CBSE Class 12 · 2016 · All India · SemiconductorsShort Answer

(i) In a conductor the valence and conduction bands overlap (or the conduction band is partly filled), so there is no forbidden gap and conduction is easy.
In a semiconductor a small forbidden gap ($\approx 1\mathrm{eV}$) separates a filled valence band from an empty conduction band, so only a few carriers are available at room temperature.
(ii) Reading the waveforms: $(A,B)=(1,1)\to Y=0$ and all other combinations give $Y=1$.
This is the NAND operation $Y=\overline{A\cdot B}$; its symbol is an AND symbol with an output bubble.
$\boxed{\text{(i) overlap vs small gap; (ii) NAND gate.}}$