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Boolean AND inverses

If we AND together value and its inverse (NOT , or ), we get , 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 and one is true, so they’re NOT both true.

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