How do I minimize this Boolean expression?

Question

How do I minimize the following expression $$W'\cdot X'+ X'\cdot Y' + W'\cdot Z' + Y \cdot Z$$

where $\cdot$ stands for Logical AND, $'$ stands for Negation and $+$ stands for Logical OR.

Answer 1

$$W'\cdot X'+ X'\cdot Y' + W'\cdot Z' + Y \cdot Z = \text{ (Adjacency)}$$

$$W'\cdot X' \cdot Y + W'\cdot X' \cdot Y' + X'\cdot Y' + W'\cdot Z' + Y \cdot Z = \text{ (Adjacency)}$$

$$W'\cdot X' \cdot Y \cdot Z + W'\cdot X' \cdot Y \cdot Z' + W'\cdot X' \cdot Y' \cdot Z + X'\cdot Y' + W'\cdot Z' + Y \cdot Z = \text{ (Absorption x 3)}$$

$$X'\cdot Y' + W'\cdot Z' + Y \cdot Z $$

Just to be clear, in the last step:

$X' \cdot Y'$ absorbs $W'\cdot X' \cdot Y'$

$W'\cdot Z'$ absorbs $W'\cdot X' \cdot Y \cdot Z'$

$Y \cdot Z$ absorbs $W'\cdot X' \cdot Y \cdot Z$

You can also use the Consensus Theorem:

$$P \cdot Q + Q' \cdot R + P \cdot R = P \cdot Q + Q' \cdot R$$

Applied to your statement:

$$W'\cdot X'+ X'\cdot Y' + \color{green}{W'\cdot Z' + Y \cdot Z} = \text{ (Consensus)}$$

$$\color{green}{W'\cdot X'+ X'\cdot Y'} + W'\cdot Z' + Y \cdot Z + \color{green}{W' \cdot Y}= \text{ (Consensus)}$$

$$X'\cdot Y' + \color{green}{W'\cdot Z' + Y \cdot Z + W' \cdot Y}= \text{ (Consensus)}$$

$$X'\cdot Y' + W'\cdot Z' + Y \cdot Z$$