3$^{rd}$ NOR gate can replaced by Bubbled AND gate ==> those bubble will cancel the Bubbles of 1,2 gates.
∴ 1$^{st}$ is AND gate, 2$^{nd}$ is OR gate, 3$^{rd}$ is AND gate.
from 1$^{st}$ gate o/p is = AB
from 2$^{nd}$ gate o/p is = $\overline{A}$ + B
==> o/ of 3$^{rd}$ gate = AB . ( $\overline{A}$ + B ) = AB