Solution

Given Boolean expression is

$\overline{A}\cdot B+A\cdot \overline{B}+A\cdot B$

Now, group the last two terms:

$= \overline{A}\cdot B+A(\overline{B}+B)$

Since,

$\overline{B}+B=1$

So,

$= \overline{A}\cdot B+A$

Using Boolean identity,

$A+\overline{A}B=A+B$

Therefore,

$\overline{A}\cdot B+A\cdot \overline{B}+A\cdot B=A+B$