Boolean Logic Equation
In Boolean Algebra we have:

\begin{align*}
a \cdot b &amp;= \min{(a,b)}\\
a + b &amp;= \max{(a,b)}
\end{align*}



So, by the first definition it's obvious that:

$$ x \cdot 1 = \min{(x,1)} = x$$

Since $x \leq 1$.

By the same reasoning:

$$1 + y = \max{(1,y)} = 1$$
since $y \leq 1$.

So you have:

\begin{align*}
x + x \cdot y &amp;= (x \cdot 1) + (x \cdot y)\\
&amp;= x \cdot \color{red}{(1 + y)}\\
&amp;= x \cdot \color{red}{1}\\
&amp;= x \cdot 1 = x
\end{align*}