Boolean OR inverses

If we OR together value x and its inverse (NOT x, or \overline{x}), we get 1, because:

That’s because OR requires at least one side to be true if we want a true result, and we know that one of the sides is true and one is false, so at least one side is true.

A + \overline{A} = 1

Simplifying, just replace anywhere we have something ORed with its inverse with just 1. For example, \overline{A} + A simplifies to just 1.

flashcards

QuestionAnswer
What happens when we OR a boolean value x with its inverse \overline{x}?The result is always 1, because x + \overline{x} = 1.
This works since one of x or \overline{x} is always true, satisfying the OR condition.
What is the Boolean logic rule for A + \overline{A}?A + \overline{A} = 1
How do you simplify any expression where a term is ORed with its own inverse?Replace the entire ORed pair with just 1.
For example, \overline{A} + A simplifies to 1.