Boolean AND dominance

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

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.

flashcards

QuestionAnswer
Boolean AND dominanceWhen a boolean variable x is ANDed with 0, the result is always 0.
* 0 \cdot 0 = 0
* 1 \cdot 0 = 0
* So x \cdot 0 = 0
Why does x \cdot 0 = 0 always hold?Because AND requires both operands to be true for a true result. Since one operand is false (0), the result is always false regardless of x.
What is the formal expression for Boolean AND dominance?A \cdot 0 = 0
How do you simplify an expression like A \cdot 0?Replace A \cdot 0 with just 0.