Boolean OR identity

The identity of the OR operation is the value that, when we combine it with value using the OR operation, we get back again.

That’s because zero is treated as false, and because either side has to be true for the OR to be true, if is , then the OR will be , and if is , then the OR result will be , so the result is just .

In the case of OR, it’s , because:

This means that if we have a value and we OR it with , we get back again:

Boolean simplification

Now we know that, we can simplify any expression that has something ORed with . Whenever we see something ORed with , we can just remove the and keep the other value.

For example, if we have , we can simplify it to just .