Boolean Algebra : Using identities, prove x(x + y) = x
Solution:
$$ \begin{align}x(x+y) 
&amp;= (x\cdot x)+(x\cdot y) \quad\text{[Distributive Law]} \\
&amp;= x + (x\cdot y) \quad\text{[Idempotent Law]} \\
&amp;= x \cdot (1+y) \quad\text{[Distributive Law]}\\
&amp;= x \cdot 1 \quad\text{[Property of 1]} \\
&amp;= x \quad\text{[Property of 1]}
\end{align}$$