Boolean AND dominance

The booleans dominance law says that when we have a value x ANDed with 0, the result is always 0, because:

• 0 \cdot 0 = 0
• 1 \cdot 0 = 0
• So x \cdot 0 = 0

This is because the AND requires both sides to be true if we want a true result, but we already know one of the sides is false, so the result must also be false, we don’t need to know the value of x to know that the result is 0.

A \cdot 0 = 0

We can replace anywhere we have something ANDed with 0 with just 0 in order to simplify expressions. For example, A \cdot 0 simplifies to just 0.