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Boolean AND dominance

The boolean dominance law says that when we have a value ANDed with , the result is always , because:

  • So

This is because the AND requires both sides to be true if we want a true result, but we already know one of the sides is false, so the result must also be false, we don’t need to know the value of to know that the result is .

We can replace anywhere we have something ANDed with 0 with just 0 in order to simplify expressions. For example, simplifies to just .