In order to solve a Boolean equation we need to understand some rules. These rules help us to solve the equation by reducing the terms in equation.

Rule 1: This rule states that if we add a term say 'A' to 1, then we will get 1 as result

A + 1 = 1.

Rule 2: If we multiply a term with 1, we get A as a result.

1A = A.

These are identity rules.

Rule 3: If we add a term to its complimented form then we get 1 as a result.

A + A’ = 1,

Rules 4: If we have an equation as (A + B) (A + C) then we can represent it as (A + BC). This is called product of sum expression.

Rule 4: If we have an equation as A + A’B then can be written as A + B.

A + A’B = A + B.

Now let us take an example understand the process of finding solution of a Boolean expression.

Assume that we have a Boolean equation (A + B) (A + C), we can reduce this equation as:

We can see that it is a product of sum expression. We will apply rules on this expression. First we will multiply the terms:

AA + AC + AB + BC.

Applying the identity rule on AA = A.

A + AC + AB + BC,

Applying the rule A + AB = A,

A + AB + BC.

Applying the rule A + AB = A

A + BC. This is the solution of Boolean equation.