Prove:

A × B = ∅ if and only if A = ∅ or B = ∅.

Printable View

- March 4th 2009, 10:00 PMjacob233Cartesian Proof Sets
Prove:

A × B = ∅ if and only if A = ∅ or B = ∅. - March 4th 2009, 11:15 PMkalagota
maybe this will help you..

- March 4th 2009, 11:31 PMJhevon
i would do this by proving the forward direction using the contrapositive, and the converse via a direct proof.

at some point in your text you should have it written that for every set . this should help you prove the converse directly.

for the forward direction, assume NOT or . then by DeMorgan's laws, we have that AND . now if both and are nonempty, what can you say about ? - March 5th 2009, 05:51 PMkalagota
here is another hint: it should be trivial that

use this hint and the previous hint i posted and you shall have the (two way) proof i am thinking..