This question consists of two parts which are not necessarily related.

Part I

A combinational logic circuit is shown in Figure $2.$

$[$a$]$ Write a general Boolean algebra expression for the output $F$ as a function of the inputs $A,B.$

$[$b$]$ UsingDeMorgan's theorems and other Boolean identities, simplify the expression obtained in $[$a$].$ Is there a single gate which can replace the network shown?

$[$c$]$ Generate a truth table giving the logic levels at points $C,D,E$ and $F$ for inputs $A,B.$

Part II

Design a $2-$input exclusive or $($EOR$)$ gate using only $2-$input NOR gates.

$[$d$]$ Develop the truth table for the gate.

$[$e$]$ Write a general Boolean algebra expression for the output as a function of the inputs.

$[$f$]$ Using DeMorgan's theorems and other Boolean identities, modify the expression obtained in $[$e$]$ to provide a solution which can be implemented with NOR gates.

$[$g$]$ Draw the circuit diagram for the final gate array.

Figure $2$ Combinational Logic circuit