Consider the following quantum circuit:

a$)$ Find the output of the circuit when $|a$: and $|b$:$.(1$ Mark$)$

b$)$ Find the output of the circuit when $|a$: and $|b$:$.(1$ Mark$)$

c$)$ Find the output of the circuit when $|a$: and $|b$:$.(1$ Mark$)$

d$)$ Find the output of the circuit when $|a$: and $|b$:$.(1$ Mark$)$

e$)$ Based on your answers in the previous parts, explain the function of the circuit. $)2$ Marks$)$