How can I prove this. what is the way? im up to the second last line. and i dont actually know how can x * (1 + y) then the y just disappears into x * 1. x + x * y = xx + x * y = (x * 1) + (x * y)          = x * (1 + y)          = x * 1 [THIS LINE]          = xthanks
Boolean Logic Equation
logic;boolean algebra
In Boolean Algebra we have:\begin{align*}a \cdot b &= \min{(a,b)}\\a + b &= \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 &= (x \cdot 1) + (x \cdot y)\\&= x \cdot \color{red}{(1 + y)}\\&= x \cdot \color{red}{1}\\&= x \cdot 1 = x\end{align*}