Identify the logic gates represented by the given circuits $(a)$ and $(b)$ and write their truth tables.

(N/A) For circuit $(a)$:
Input $A$ is connected to both inputs of the $NOR$ gate. The output $Y$ is given by $Y = \overline{A+A} = \bar{A}$.
The truth table is:

$A$	$Y(=\bar{A})$
$0$	$1$
$1$	$0$

This is the truth table of a $NOT$ gate. Hence,circuit $(a)$ functions as a $NOT$ gate.
For circuit $(b)$:
$A$ and $B$ are inputs. The first two $NOR$ gates act as $NOT$ gates,producing outputs $\bar{A}$ and $\bar{B}$.
These are inputs to the final $NOR$ gate. The output $Y$ is:
$Y = \overline{\bar{A}+\bar{B}} = \overline{\overline{A \cdot B}} = A \cdot B$ (using De Morgan's theorem).
The truth table is:

$A$	$B$	$Y(=A \cdot B)$
$0$	$0$	$0$
$0$	$1$	$0$
$1$	$0$	$0$
$1$	$1$	$1$

This is the truth table of an $AND$ gate. Hence,circuit $(b)$ functions as an $AND$ gate.