Each of the two inputs $A$ and $B$ can assume values either $0$ or $1$. Then which of the following will be equal to $\bar{A} \cdot \bar{B}$?

For the given truth table, where $A, B$, and $C$ are inputs and $Y$ is the output, determine the functional form of the circuit.

$A$	$B$	$C$	$Y$
$0$	$0$	$0$	$1$
$0$	$0$	$1$	$1$
$0$	$1$	$0$	$0$
$0$	$1$	$1$	$0$
$1$	$0$	$0$	$1$
$1$	$0$	$1$	$1$
$1$	$1$	$0$	$0$
$1$	$1$	$1$	$0$

The circuit diagram shows a logic combination. Initially, for inputs $P, Q, R$ and $S$ all at state $1$, the outputs are $X=1, Y=1$ and $Z=0$. When inputs $P$ and $R$ change to state $0$ while inputs $Q$ and $S$ remain at state $1$, what are the new states of outputs $X, Y$ and $Z$?

Which of the following circuits has the same output as that of the given circuit?

The truth table given below is for which gate?
$A: 0, 0, 1, 1$
$B: 0, 1, 0, 1$
$C: 1, 1, 1, 0$

Identify the logic operation performed by the given circuit.