Prove or find counterexamples

• December 2nd 2008, 08:18 AM
mbcsantin
Prove or find counterexamples
If A x B = empty set then A = empty set or B = empty set.
• December 2nd 2008, 08:23 AM
vincisonfire
What is the "x"?
Is it intersection? union?
Are A and B groups, sets, rings?
• December 2nd 2008, 08:33 AM
mbcsantin
Quote:

Originally Posted by vincisonfire
What is the "x"?
Is it intersection? union?
Are A and B groups, sets, rings?

the x stands for multiplication.

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

or - stands for Union but in this question i don't think the "or" means Union in this question though.
although that's actually a very good question! hmmm..
• December 2nd 2008, 08:42 AM
Plato
Quote:

Originally Posted by mbcsantin
the x stands for multiplication.

Quote:

Originally Posted by mbcsantin
If A multiply B = empty set then A = empty set or B = empty set.

No it does not stand for multiplication in a set theoretic context.
It is a cross product: $A \times B = \left\{ {\left( {a,b} \right):a \in A\,\& \,b \in B} \right\}$.
Now it is perfectly clear that if either set is empty then the cross product is empty and visa versa.