Boolean OR identity

The identity of the OR operation is the value that, when we combine it with value x using the OR operation, we get x 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 x is 0, then the OR will be 0, and if x is 1, then the OR result will be 1, so the result is just x.

In the case of OR, it’s 0, because:

• 0 + 0 = 0
• 1 + 0 = 1

This means that if we have a value x and we OR it with 0, we get x back again:

• 0 + 0 = 0
• 1 + 0 = 1

A + 0 = A

Boolean simplification

Now we know that, we can simplify any expression that has something ORed with 0. Whenever we see something ORed with 0, we can just remove the 0 and keep the other value.

For example, if we have 0 + A, we can simplify it to just A.