If A x B = empty set then A = empty set or B = empty set.

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- Dec 2nd 2008, 08:18 AMmbcsantinProve or find counterexamples
If A x B = empty set then A = empty set or B = empty set.

- Dec 2nd 2008, 08:23 AMvincisonfire
What is the "x"?

Is it intersection? union?

Are A and B groups, sets, rings? - Dec 2nd 2008, 08:33 AMmbcsantin
- Dec 2nd 2008, 08:42 AMPlato
**No it does not stand for multiplication**in a set theoretic context.

It is a*cross product*: $\displaystyle A \times B = \left\{ {\left( {a,b} \right):a \in A\,\& \,b \in B} \right\}$.

Now it is perfectly clear that if either set is empty then the cross product is empty and visa versa.