A logic circuit is given below.

TVE$=$ NAND

a$)$ Find the expression of the output function $f$ of the circuit in terms of the variables a$,$ b and c $.$

b$)$ Implement the circuit with only two$-$input NAND gates.

c$)$ Implement the circuit with only two$-$input NOR gates.

d$)$ Compare the given circuit, NAND and NOR designs, in terms of design criteria. Explain which design would be a more appropriate choice and why