NIMCET 2011 Question Paper with solutions

The given Boolean expression is
Let $\mathit{E}=\mathit{x}\cdot \left(\mathit{x}+\mathit{y}\right)$
$=\mathit{x}\cdot \mathit{x}+\mathit{x}\cdot \mathit{y}$ "by distributive law"
$=\mathit{x}+\mathit{x}\cdot \mathit{y}$ "by idempotent law"
$=\mathit{x}\cdot \left(1+\mathit{y}\right)$ "by distributive law ${}^{\prime \prime }$
$=\mathit{x}\cdot 1$ "by boundless law"
$=\mathit{x}$ "by identity law"
which is the required simplified form of E.