In the given logical circuit, all logic gates are NAND gate.

Here, the inputs $A$ and $B$ are inverted using NOT gate (made using NAND gate), then $\overline{A}$ and $\overline{B}$ are applied as inputs in other NAND gate.

So, $\left(\overline{A.A}\right)=\overline{A}$ and $\overline{B.B}=\overline{B}$

Output at $Y$ is $\left(\overline{A}.\overline{B}\right)=A+B$.

The above boolean expression is for OR gate.

Truth table of OR gate is 

The output waveform is shown below.