Question

By using Bolean Algebra prove that $\overline{A}B+A\overline{B}+AB=A+B$.

Answer 1

$f=\overline{A}B+A\overline{B}+AB$
$=\overline{A}B+(\overline{B}+B)A$ $\overline{B}+B=1$
$=\overline{A}B+A$ $[\because A+(BC)=(A+B\left)\right(A+C\left)\right]$
$=(A+\overline{A})(A+B)$
$=A+B$