Let A and B be nonempty sets, and let .

and is logically correct.

Now if C and D are nonempty sets, and that .

Will the following be true?

and .

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- Feb 22nd 2010, 05:17 PMnoviceElement in a Set
Let A and B be nonempty sets, and let .

and is logically correct.

Now if C and D are nonempty sets, and that .

Will the following be true?

and . - Feb 22nd 2010, 06:20 PMDrexel28
- Feb 23rd 2010, 06:55 AMPlato
- Feb 23rd 2010, 08:26 AMnovice
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? - Feb 23rd 2010, 08:51 AMPlato
- Feb 23rd 2010, 09:07 AMnovice