Boolean AND zero

If we have an expression like:

A\cdot 0

…then for any value of A, we are ANDing it with 0. If we and anything with 0, then we just get 0 (because at least one is 0, so AND cannot be true).

We know that, because of the AND truth table:

• 1 AND 0 = 0
• 0 AND 0 = 0, so:
• A AND 0 = 0
• (because A must represent either a 1 or a 0)

In short:

A\cdot0=0

We can use this to simplify boolean algebra!

We can replace anywhere we see A\cdot0 with 0