Clarification on the dual expression of a Boolean algebra.

Question

I need to get some clarification on if i got some answers right.

Question:

Let B be a Boolean algebra. For x, y, z ∈ B find the dual expressions of

$i)\; (x + \bar y) · \overline {(\bar z + y)}\quad $

$ii) \;(1 + x) · y + x · \bar y · z$

$iii) \;(x · y + 1) · (0 + x) · z$

My answer:

$i) \; x\bar y + \overline {\bar zy}$

$ii) \; (0 · x) + yx + \bar y + z$

$iii) \; x + (y · 0) + (1 · x) + z$

Are the answers sufficent or do i have to do more or other calculations?

Answer 1

Your second answer appears to contain a mistake, it is missing a pair of brackets. The duel of is $(1)$ is $(2)$.

\begin{equation}\tag{1} (1 + x) \cdot y + x \cdot \bar y \cdot z \end{equation} \begin{equation}\tag{2} \big((0 \cdot x) + y\big)\cdot\big( x + \bar y + z\big) \end{equation}

While your answers (after correcting the typo) are sufficient, you could go one step further and simplify them if you felt like it.