Identify the gate and match A, B, Y in bracket to check.

The given diagrams involve 2 gates.
The first 1 is an AND gate followed by a NOT Gate, with the compliment of the output of first gate used as an input to the other gate which is NAND gate as NOT gate.
We consider the 4 combinations
$A=1,B=1,AB=1,(AB{)}^{\prime }=0,\overline{AB}=1,Y=0$
$A=1,B=0,AB=0,(AB{)}^{\prime }=1,\overline{AB}=0,Y=1$
$A=1,B=0,AB=0,(AB{)}^{\prime }=1,\overline{AB}=0,Y=1$
$A=0,B=0,AB=0,(AB{)}^{\prime }=1,\overline{AB}=0,Y=1$

The above configuration represents that of an AND gate.