Plato,
Thank you for pointing the De Morgan's Law. While we are at it, I would like to discuss it with you in regard to a cross product.
Since the De Morgan's Law said .
Now let and be nonempty sets and let . We say that , which gives us or .
So and . Consequently . We have just shown that , but according to the De Morgan's Law
is false.
Suppose that I made , it should follow that the logic equivalence is or .
Consequently, or cannot be .
Do you agree?