Boolean AND identity

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

In the case of the AND operation, the identity is , because:

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

Boolean simplification

Knowing this identity can help us simplify expressions. Whenever we see something ANDed with , we can just remove the and keep the other value.

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