For the logic circuit shown in the figure,the Boolean expression is:

The new switching circuit for the following circuit by simplifying the given circuit is

$A$ truth table is given below. Which of the following logic gates corresponds to this truth table?
$A: 0, 1, 0, 1$
$B: 0, 0, 1, 1$
$Y: 1, 0, 0, 0$

The truth table of the following circuit is

The truth table for the given circuit of four $NAND$ gates is:

$A$ $NOR$ gate and a $NAND$ gate are connected as shown in the figure. Two different sets of inputs are given to this setup. In the first case, the inputs to the gates are $A=0, B=0, C=0$. In the second case, the inputs are $A=1, B=0, C=1$. The output $D$ in the first case and second case respectively are