Q.According to the laws of Boolean algebra, the expression $(A + AB)$ is equal to :

Boolean algebra (George Boole, 1854) is an algebra built entirely on the binary choice 0/1, governing the three basic operations NOT ($\overline{A}$), OR ($A+B$) and AND ($A\cdot B$). Its laws: COMPLEMENT law ($A\cdot\overline{A}=0$, $A+\overline{A}=1$); OR laws ($A+0=A$, $A+1=1$, $A+A=A$); AND laws ($A\cdot0=0$, $A\cdot1=A$, $A\cdot A=A$); COMMUTATIVE ($A+B=B+A$, $A\cdot B=B\cdot A$); ASSOCIATIVE ($A+(B+C)=(A+B)+C$, $A\cdot(B\cdot C)=(A\cdot B)\cdot C$); and DISTRIBUTIVE ($A(B+C)=AB+AC$, and the Boolean-specific $A+BC=(A+B)(A+C)$, which has no ordinary-arithmetic analogue). These laws simplify complicated logic expressions -- and hence the physical gate count needed to build them -- e.g. $AC+ABC=AC(1+B)=AC\cdot1=AC$ (using OR law 2 then AND law 2), collapsing a 3-input-AND-plus-2-input-AND-plus-OR circuit down to a single 2-input AND gate. …