Question 3.10: Simplify the Boolean expression F = AB + BC + BC + AB...
Simplify the Boolean expression F=A\bar{ B}+B \bar{C}+\bar{B} C+\bar{A} B
= A\overline{{{B}}}(C+\overline{{{C}}})+B\overline{{{C}}}(A+\overline{{{A}}})+\overline{{{B}}}C+\overline{{{A}}}B Rule 8 : 1=A + \overline{A}
= {{A}}{\bar{B}}C+A{\bar{B}}{\bar{C}}+A{{B}}{\bar{C}}+{\overline{{A}}}B{\overline{{C}}}+{\overline{{B}}}C+{\overline{{A}}}B Distributive law
= (A\overline{{{B}}}C+\overline{{{B}}}C)+(A\bar{B}\bar{C}+A{B}\overline{{{C}}})+(\overline{{{A}}}B\overline{{{C}}}+\overline{{{A}}}B) Associative law
= {\overline{{B}}}C+A{\overline{{C}}}+{\overline{{A}}}B Factoring and drop the 1
The simplification using Boolean algebra depends on your experience. It requires that you are familiar with the laws, the rules and the theorems of Boolean algebra and obtain skill by doing more exercises.