AND absorption

AND absorption

When we have a boolean expression in the form A \cdot (A + B), we can simplify it using a rule called absorption.

We know that both A and the thing on the right must be true for the whole expression to be true. But if just A is true, then the right hand side A+B is also true, so we can just ignore it and simplify the expression to just A.

A \cdot (A + B) = A

OR absorption

When we have a boolean expression in the form A + (A \cdot B), we can also simplify it using absorption.

We know that either A or the thing on the right must be true for the whole expression to be true. But if just A is true, then the right hand side A \cdot B is also true, so we can just ignore it and simplify the expression to just A.

A + (A \cdot B) = A