$2\mathrm{.}23.$ Derive the truth table for the following logic gates.

a$)$ A $4-$input AND gate.

b$)$ A $4-$input NAND gate.

c$)$ A $4-$input NOR gate.

d$)$ A $4-$input xOR gate.

e$)$ A $4-$input xNOR gate.

f$)$ A $5-$input Xor gate.

g$)$ A $5-$input xNOR gate