Boolean AND identity

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

In the case of the AND operation, the identity is 1, because:

This means that if we have a value x and we AND it with 1, we get x back again:

A \cdot 1 = A

Boolean simplification

Knowing this identity can help us simplify expressions. Whenever we see something ANDed with 1, we can just remove the 1 and keep the other value.

For example, if we have the expression A \cdot 1, we can simplify it to just A.

Question	Answer
Boolean AND identity	The identity of the AND operation is 1, because 0 \cdot 1 = 0 and 1 \cdot 1 = 1. Therefore, A \cdot 1 = A.
How can you simplify the expression A \cdot 1?	It simplifies to just A because the identity of AND is 1, so ANDing a value with 1 returns the original value.
What is the general rule for simplification using the Boolean AND identity?	Whenever we see something ANDed with 1, we can just remove the 1 and keep the other value.